A bibliography on spline functions II

van Rooij, P.L.J.; Schurer, F.

Published: 01/01/1973

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Citation for published version (APA):van Rooij, P. L. J., & Schurer, F. (1973). A bibliography on spline functions II. (EUT report. WSK, Dept. ofMathematics and Computing Science; Vol. 73-WSK-01). Eindhoven: Technische Hogeschool Eindhoven.

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TECHNISCHE HOGESCHOOL EINDHOVEN

NEDERLAND

ONDERAFDELING DER WISKUNDE

TECHNOLOGICAL UNIVERSITY EINDHOVEN

THE NETHERLANDS

DEPARTMENT OF MATHEMATICS

A bibliography on spline functions. II

by

P.L.J. van Rooij and F. Schurer

T.H.-Report 73-WSK-01

January 1973

I

Introduction

About one year ago we published a report* that contained a bibliography

on spline functions. The compilation included three kinds of publications,

namely, papers in mathematical periodicals, books, and doctoral disserta­

tions, all of which had appeared before January 1, 1971. For various reasons

a fourth kind of publication, reports, was not included in the bibliography.

The report was sent to a number of mathematicians working in the field

of spline approximation with a request to suggest corrections and improve­

ments. As a result of that, we generously received a large number of comments

on the report. Although it is impossible here to mention all those who re­

sponded, we in particular want to thank B.I. Kvasov, G. Micula, J. Nitsche,

K. Scherer, LJ. Schoenberg, L.L. Schumaker, E. Stark,and R.S. Varga for

their contributions. Especially B.l. Kvasov supplied us with most useful

information on spline papers written by Russian authors.

The present report is a revised and augmented version of the first edi­

tion. To the best of our knowledge we included all papers, books and doctoral

dissertations that appeared be~ore January 1,1972 and which deal with the

theory and application of spline approximation. As before, reports were not

included in the bibliography.

The main part of the report consists of a list ordered chronologically

and, 'for publications that have appeared in the same year, alphabetically.

Moreover, there is an index of authors together with a coded list of the

papers they have contributed to the field. Of course, the decision for in­

cluding or not a particular publication was sometimes rather difficult and

the outcome may be subject to criticism. In this respect we greatly valued

all the advice we received concerning the contents of the bibliography, but

we did not invariably follow it. Thus the responsibility for the omissions

and errors in the present report is entirely ours, while the improvements

are largely due to those who responded.

As we already remarked in the first version of the bibliography there

are several other sources where one can find elaborate references to the

literature on spline functions. In this respect we want to mention the

bibliographies in the monograph of Ahlberg, Nilson and Walsh [67-2J and l.n

* A bibliography on spline functions. T.R.-Report 71-WSK-02.

II

the books edited by Grevillc 169-:321 and Schoenberg [69-86J, respectively.

OtlU.'l- lIseful information is contailled in tile btbliography "Recent pUblica­

tions 1n approximation tllcory willi l'lllpll:Jsis on computer. applications", (;om-

piled by C.L. Lawson . (Computing Reviews 9 (1968), 691-699). One may also

consult the paper by Schultz and Varga [67-37]. In addition to these sources,

we particularly want to call the reader's attention to the fine bibliography

1n the monograph of Sard and Weintraub [71-96J which recently appeared.

The journal abbreviations are those given in Hathematical Reviews 41

(1971), 1939-1960. We have strived to add to each publication one or more

references to reviews 1n Mathematical Reviews (MR), Zentralblatt fur Mathe­

matik (Zb), Referativnyi 1urnal Matematika (RJH) , Computing Reviews (CR),

Computer Abstracts eCA) , Bulletin Signaletique 110 CBS) and Dissertation

Abstracts (DA). In comparison with the first version of the bibliography the

references to reviews in the Referativnyi Zurnal Matematika are new. An

asterisk * indicates that the publi is a doctoral dissertation,or a

book that is mainly concerned with spline functions.

The compilation contains a total number of 614 items, of which 532 have

been published during the years 1966-1971. Although the bibliography is

certainly not complete, we hope that it gives a reasonable survey of the

existing literature on spline functions until January 1, 1972.

During the project Miss Yvonne Naus of the mathematics library of the

Technological University Eindhoven has been of valuable assistance to us. It

18 a pleasure to thank her again for all the work she has done.

Finally, we convey our gratitude to Mrs. E.E.F.M. Baselmans~Weijers for

her superb technical typing.

- 1 - 1902

Bibliography

1902

I. Wirtinger, W. Einige Anwendungen der Euler-Maclaurin'schen Summenformel, insbesondere auf eine Aufgabe von Abel. Acta Math. 26 (1902), 255-271.

1904

1. Runge,·C. Theorie und Praxis der Reihen. § 20. Goschen'sche Verlagshandlung, Leipzig, 1904.

1938

I. Quade, W.; Collatz, L. Zur lnterpolationstheorie der reel len periodischen Funktionen. S.-B. Preuss. Akad. Wiss. Phys.-Math. KI. 30 (1938), 383-429. (Zb ~, p. 397.)

I. Favard, J. Sur l'interpolation. J. Math. Pures Appl. 19 (MR l, p. 114; Zb 23, p.

1. Popoviciu, T.

1940

(1940), no. 9, 281-306. 24. )

1941

Notes sur les fonctions convexes d'ordre superieur. IX. Bull. Math. Soc. Sci. Math. R.S. Roumanie 43 (1941), 85-141. (MR 7.., p. 1 16. )

1944

1. Love, A.E.R. A treatise on the mathematical theory of elasticity. § 262; p. 404. Dover, New York, 1944.

1946

1. Schoenberg, I.J. Contributions to. the problem of approximation of equidistant data by analytic functions. Part A: On the problem of smoothing of graduation. A first class of analytic approximation formulae. Quart. Appl. Math. 4 (1946), 45-99. (MR 7.., p. 487.) -

2. Schoenberg, I.J. Contributions to the problem of approximation of equidistant data by analytic functions. Part B: On the problem of osculatory interpolation. A second class of analytic approximation formulae. Quart. Appl. Math. 4 (1946), 112-141. (MR~, p. 55.) -

- 2 - 1949

1949

I. Sard, A. Best approximate integration formulas; best approximation formulas. Amer. J. Math. 71 (1949), 80-91. (MR 1£, p. 576;:Zb 39, p. 341.)

2. Schoenberg, I.J.; Whitney, A. Sur la positivite des determinants de translations des fonctions de frequence de Pi5lya, avec une application a une probleme d' interpolatio.n. C.R. Acad. Sci. Paris Sera A 228 (1949), "1996-1998 •

. (ViR.!.!., p. 86.) -

3. Synge, J.L.; Griffith, B.A. Principles of mechanics, pp. 92-98. McGraw-Hill, New York, 1949.

1950

1. Meyers, L.F.; Sard, A. Best approximate integration formulas. J. Math. and Phys. 29 (1950), 118-123. (MR ll, p. 83; Zb 39, p. 342.)

2. Meyers, L.F.; Sard, A. Best interpolation formulas. J. Math. andPhys. 29 (1950), 198-206. (HR ll, p. 396; Zb 40, p. 28.)

1953

1. Schoenberg, I.J.; Whitney, A. On P6lya frequency functions. III: The positivity of translation deter­minants with an application to the interpolation problem by spline curves. Trans. Amer. Math. Soc. 74 (1953), 246-259. (MR~, p.732; RJM (1953);" 1154.)

]954 v

I. ShaLdaeva, T.A. * Most precise quadrature formulae for certain classes of functions

(Russian) (Doctoral dissertation). Leningrad State Univ., Leningrad, 1954.

1956

I. Sokolnikoff, I.S. Mathematical theory of elasticity, p. 1. McGraw-Hill, New York, 1956.

1957

1. Holladay, J.C. A smoothest curve approximation. Math. Tables Aids Comput. II (1957), 233-243. (MR 20, 414; Zb 84, p. 349;-RJM (1960), 5897.)

- 3 -

2. Ionescu, D.V. Numerical quadrature (Roumanian). Editura Tehnica, Bucure~ti, 1957.

1958

" I. Nikolskii, S.M. Quadrature formulae (Russian). Moscow, 1958.

1958

'Translated as International monographs on advanced mathematics and physics, no. 29. Rindustan Publ. Corp., Delhi (India), 1964.

2. Schoenberg, I.J. Spline functions, convex curves and mechanical quadrature. Bull. Amer. Math. Soc. 64 (1958), 352-357. (MR 20, 7174; Zb 85, p.~37; RJM (1959), 10957.)

1959

1. Ciesielski, Z.; Musielak, J. On absolute convergence of Raar series. Colloq. Math. 7 (1959), 61-65. (MR 22, 863; Zb 90, p. 281.)

2. Ciesielski, Z. On Raar functions and on the Schauder basis of the space C[O,I]. Bull. Acad. Polon. Sci. Sere Sci. Math. Astronom. Phys. 7 (1959), 227-232. (MR 24, A 1599; Zb ~, p. 54; RJM (1960), 4232.) -

3. Golomb, M.; Weinberger, R.F. Optimal approximation and error bounds. in: On numerical approximation (Proc. Symp. Math. Res. Center, Univ. Wisconsin, April 1958); ed. by R.E. Langer, pp. 117-190. Univ. of Wisconsin Press, Madison, 1959. (MR~, 12697; Zb 92, p. 58; RJM (1960), 12183.)

4. Krylov, V. 1.

v

Approximate calculation of integrals (Russian). Gos. Izdat. Fiz.-Mat. Lit. Mosk., 1959. (MR 22, 2002.) Translated at Macmillan. New York, 1962. (MR~, 2008.)

5. Shaidaeva, T.A. Quadrature formulae with least error estimate for some classes of func­tions (Russian). Trudy Mat. Inst. Steklov 53 (1959), 313-341. (MR~, 200 I • )

6. Simonsen, W. On numerical differentiation of functions of several variables. Skand. Aktuarietidskr. 42 (1959), 73-89. (RJM (1961), 6V251.) --

- 4 - 1960

1960

I. Birkhoff, G.; Garabedian, H.L. Smooth surface interpolation. J. Math. and Phys. 39 (1960), 258-268. (MR~, 10151; Zb 161, p. 129; RJM (1962), 6VI88.)

2. Ciesielski, Z. On the isomorphisms of the spaces Ha and m. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. ! (1960), 2]7-222. (MR 24, A2234; Zb 93, p. 123; RJM (1961), 7B413.)

3. Ciesielski, Z. Some properties of Schauder bases of the space C[O,I]. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. ! (1960), 141-144. (MR 26, 5417; Zb 21, p. 70; RJM (1961), 4BI2.)

4. Johnson, R.S. On monosplines of least deviation. Trans. Amer. Math. Soc. 96 (1960), 458-477. (HR 23, A270; RJM (1963)-, 4BIOI.)

5. Rutishauser, H. Bemerkungen zur glatten Interpolation. Z. Angew. Math. Phys. II (1960), 508-513. (MR 26, 883; RJM (1961~ 12V311.)

6. Schwerdtfeger, H. Notes on numerical analysis. II: Interpolation and curve fitting by sectionally linear functions. Canad. Math. Bull. 3 (1960), 41-57. (Zb 96, p. 103; RJM-(I961), 8V245.)

1961

" I. Brudny~, Yu.A.; Gopengauz, I.E. Approximation by piecewise polynomial functions. Dokl. Akad. Nauk SSSR ~ (1961), 1283-1286 (Russian). Translated as Soviet Math. Dokl. 2 (1961), 1627-1630. (MR 24, A2175; RJM (1962), 9B82.)-

2. Schwerdtfeger, H. Notes on numerical analysis. III: Further remarks on sectionally linear functions. Canad. Math. Bull. 4 (1961), 53-55. (Zb 106, p.109; RJM-(1962), 4V191.)

3. Theilheimer, F.; Starkweather, W. The fairing of ship lines on a high-speed computer. Math. Compo 15 (1961), 338-355. (MR~, B1627; Zb 109, p. 350; RJM (1962), IIVI80.)

4. Weinberger, H.F. Optimal approximation for functions prescribed at equally spaced points. J. Res. Nat. Bur. Standards Sect. B 65 (1961), 99-104. (MR~, 3616; Zb 168, p. 149; RJM (1962), 2V264.)

- 5 - 1962

1962

1. Asker, B. The spline curve, a smooth interpolating function used in numerical design of ship-lines. BIT 2 (1962), 76-82. (Zb lIZ, p. 81.)

2. Boor, C. de Bicubic spline interpolation. J. Math. and Phys. 41 (1962), 212-218. (MR 28, 1735; Zb 108, p. 271; RJM (1963), 6V48.)

3. Landis, F.; Nilson, E.N. The determination of thermodynamic properties by direct differe~tiation techniques. in: Progress in international research on thermodynamic and transport properties (Second Symp. on Thermophysical Properties); ed. by J.F. Masi and D.H. Tsai, pp. 218-227. Acad. Press, New York, 1962.

4. Petersen, I. On a piecewise polynomial approximation (Russian; Estonian and Ge~man summaries) • Eesti NSV Tead. Akad. Toimetised Fuus.-Mat. 11 (1962), 24-32. (MR 25, 3307; RJM (1963), IBI02.)

5. Walsh, J.L.; Ahlberg, J.H.; Nilson, E.N. Best approximation properties of the spline t. J. Math. Mech. 1 J (1962), 225-234. (MR 25, 738; Zb 196, p. 486; RJM (1963), 5BI12.)

1963

1. Ahlberg, J.H.; Nilson, E.N. Convergence properties of the spline fit. J. Soc. Indust. Appl. Math. 11 (1963), 95-104. (MR~, 2763; Zb 196, p. 487;-RJM (1964), 1B574.)

2. Berger, S.A.; Webster, W.C. An application of linear programming to the fairing of ships' lines. in: Recent advances in mathematical programming; ed. by R.L. Graves and P. Wolfe, pp. 241-253. McGraw-Hill, New York, 1963.

3. Boor, C. de Best approximation properties of spline functions of odd degree. J. Math. Mech. 12 (1963), 747-749. (MR~, 398Z; Z~116, p. 276; RJM (1965), 3BI51.) v

4. Brudny~, Yu.A.; Gopengauz, I.E. Approximation by piecewise polynomial functions (Russian). Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 723-746. (MR 29, 404; RJM (1964), 4B92.)-

5. Ciesielski, Z. Properties of the orthonormal Franklin system. Studia Math. 23 (1963), 141-157. (MR 28, 419; Zb !!l, p. 272; RJM (1964), 7B76.)

- 6 -

6. Sard, A. Linear approximation. Amer. Math. Soc.~Providence (R.I.), 1963. (MR 28, 1429; Zb ~, p. 54; RJM (1965), 7B88.)

7. Schaefer, H. Latteninterpolation bei einer Funktion von zwei Veranderlichen. Z. Angew. Math. Phys. 14 (1963), 90-96. (Zb 108, p. 300; RJM (1963), IIVI03.)

1964

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Fundamental properties of generalized splines. Proc. Nat. Acad. Sci. USA 52 (1964), 1412-1419. (MR 36, 6846; Zb 136, p. 362; RJM (1965), I2B472; BS 26, 9981.)

2. Ahlin, A.C. A bivariate generalization of Hermite's interpolation formula. Math. Compo 18 (1964), 264-273. (MR~, 1725;Zb 122, p. 125; RJM (1964), JOB463.)

3. Birkhoff, G.; Boor, C. de Error bounds for spline interpolation. J •. Math. Mech. 13 (1964), 827-835. (MR~, 2583; Zb 144, p. 285; RJM (1965), 8B93; BS 26, 6171.)

4. Ciesielski, Z. On the orthonormal Franklin system.

1964

Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 12 (1964), 461-464. (MR 29, 6241; Zb 138, p. 50; RJM (1965), 7B417.)

5. Ferguson, J. Multivariahle curve interpolation. J. Assoc. Comput. Mach. 11 (1964), 221-228. (MR 28, 5551; Zb 123, p.~30; RJM (196$), 4B738; CA~, 1806.)

6. Greville, T.N.E. Numerical procedures for interpolation by spline functions. SIAM .T, Num~r, Anal. 1 0.964), 53-68. (MR 36, 4784; Zb ~,-p. 336.)

7. Mehlum, E. A curve-fitting method based on a variational criterion. BIT 4 (1964), 213-223. (MR 30, 4376; RJM (1965), 9B330.)

8. P~vlHob, I. Sur l'interpolation a l'aide de polynomes raccordes. Mathematica (Cluj) 6 (1964), 295-299. (RJM (1966), 9B634.)

9. Podolsky, B.; Denman, H..H. Conditions on minimization criteria for smoothing. Math. Compo 18 (1964), 441-448. (MR 29, 5368-:)

- 7 -

10. Schechter, E. Error estimation by means of differential inequalities. Mathematica (Cluj) 6 (1964), 117-128. (Zb 221, 65119; RJM-(l966) , 12B492; BS '!:2, 6082.)

11. Schoenberg, I.J. Spline interpolation and best quadrature formulae. Bull. Amer. Math. Soc. 70 (1964), 143-148. (MR~, 394; Zb 136, p.:362; RJM (1964), IIB99.)

12. Schoenberg, I.J. Spline interpolation and the higher derivatives. Proc. Nat. Acad. Sci. USA 51 (1964), 24-28. (MR 28, 3278; Zb 136, p. 362; RJM (1965), 6BI16.)

13. Schoenberg, I.J. On best approximation of linear operators. Nederl. Akad. Wetensch. Proc. Ser. A 67 (1964), 155-163. (MR 28, 4284; Zb 146, p. 85; RJM (1965), IB93.)

14. Schoenberg, I.J. On trigonometric spline interpolation. J. Math. Mech. 13 (1964), 795-825. (MR~, 2589; Z~147, p. 321; RJM (1965), 8B92; BS ~, 6179.)

15. Schoenberg, I.J. Spline functions and the problem of graduation. Proc. Nat. Acad. Sci. USA 52 (1964), 947-950. (MR 29, 5040; Zb 147, p. 321; RJM (1965), 8B502; BS ~, 6175.)

16. Schoenberg, I.J. On interpolation by spline functions and its minimal properties.

1965

in: On approximation theory (Proc. Conf. Oberwolfach, Aug. 1963); ed. by P.L. Butzer and J. Korevaar, pp. 109-129. Birkhauser Verlag, Basel, 1964. (MR l!, 5015; Zb 147, p. 321; RJM (1966), 6B130; BS 26, 11449.)

17. Smoluk, A. On the approximation with piecewise functions (Polish). Zeszyty Nauk. Wyz. Szkol. Ekon. Wroclawiu (1964), no. 21, 107-121. (RJM (1968), 2BI49.)

1965

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Best approximation and convergence properties of higher-order spline approximations. J. Math. Mech. 14 (1965), 231-243. (MR 35, 5823; Z~141, p. 68; RJM (1966), IB116; BS 26, 13312.)

2. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Convergence properties of generalized splines. Proc. Nat. Acad. Sci. USA 54 (1965), 344-350. (MR 36, 6847; Zb 136, p. 363; RJM (1966), 7BI58; BS '!:2, 4501.)

3. MIlberg, J.H.; Nilson, E.N. Orthogonality properties of spline functions~ J. Math. Anal. Appl. II (1965),321-337. (MR 37, 660; Zb 136, p:- 48; RJM (1966), 8B124; BS '!:2, 1951.)

- 8 - 1965

4. Ahlberg, J.R.; Nilson, E.N.; Walsh, J.L. Extremal, orthogonality, and convergence properties of multidimensional splines. J. Math. Anal. Appl. 12 (1965), 27-48. (MR 1I, 661; Zb 136, ~ 48; RJM (1966), 7BI57.)

5. Atteia, M. Gen&ralisation de la definition et des proprietes des "spline fonctions". C.R. Acad. Sci. Paris Sere A 260 (1965), 3550-3553. (MR~, 3340; Zb 163, p. 377; RJM (1966), IB636; BS~, 10401.)

6. Atteia, M. "Spline-fonctions" generalisees. C.R. Acad. Sci. Paris Sere A 261 (1965), 2149-2152. (MR 35, 3341; RJM (1966), 9B517; BS ~, 2127.)

7. Birkhoff, G.; Boor, C.R. de Piecewise polynomial interpolation and approximation. in: Approximation of functions (Proc. Symp. on Appr. Functions, Gen. Motors Res. Lab., Warren, Michigan, 1964); ed. by R.L. Garabedian, pp. !64-190. Elsevier, Amsterdam, 1965. (MR 32, 6646; Zb 136, p. 47; BS ~, 7289.)

8. Collatz, L. Einschliessungssatz fur die Minimalabweichung bei der Segmentapproxima­tion. in: Simposio internazionale sulle applicazioni dell' Analisi alIa Fisica Matematica (Cagliari-Sassari, 1964), pp. 11-21. Cremonese, Rome, 1965. (MR35, 633; Zb 221,65020; RJM (1967), 2B583.)

9. Glass, J.M. * A criterion for the quantization of line-drawing data (Doctoral disser­

tation). New York Univ., Bronx, 1965.

10. Kirishchiev, R.I.; Neshevich, D.A. Some problems concerning the interpolation of functions (Russian). U~en. Zap. Kabard.-Balkar. Gos. Univ. Sere Fiz.-Mat. 24 (1965), 113-119. (RJM (1967), 5B707.)

11. Schoenberg, I.J. On monosplines of least deviation and best quadrature formulae. SIAM J. Numer. Anal. 2 (1965), 144-170. (HR 34, 2182; Zb 136,-p. 362; RJM (1966), 9B610; BS ~, 2149.)

12. Secrest, D. Numerical integration of arbitrarily spaced data and estimation of errors. SIAM J. Numer. Anal. 2 (1965), 52-68. (MR ll, 4176; Zb 135,-p. 386; RJM (1966), 7B532; BS ~, 2122.)

13. Secrest, D. Best approximate integration formulas and best error bounds. Math. Compo 19 (1965), 79-83. (MR 33, 196i";Zb 134, p. 136; RJM (1966), IB569; CA~, 831; BS~, 10411.)

14. Secrest, D. Error bounds for interpolation and differentiation by the use of spline functions. SIAM J. Numer. Anal. 2 (1965), 440-447. (MR~, 6231; Zb 144,-p. 388; RJM (1966), I1B91; BS~, 13715.)

- 9 - 1966

15. Subbotin, Yu.N •. On the relations between finite differences and the corresponding derivatives. Trudy Mat. lnst. Steklov 78 (1965), 24-42 (Russian). Translated as Extremal properties of polynomials; ed. by S.B. Ste~kin (Proc. Steklov Inst. Math. 78 (1965», pp. 23-42. Amer. Math. Soc., Providence, .] 967. -(MR 32, 7978; RJM (1966), 3BI59.)

16. Tihomirov, V.M. Sor,le problems of approximation theory. Dokl. Akad. Nauk 160 (1965), 774-777 (Russian). Translated as Soviet Math. Dokl. 6 (1965), 202-205. (RJM(l965), 7B80.) -

17. Wendroff, B. Bounds for eigenvalues of some differential operators by the Rayleigh­Ritz method. Math. Compo 19 (1965), 218-224. (MR 2l, 4J69;-RJM (1966), IB543; BS~, 13893.)

1966

1. Ahlberg, J.H.; Nilson, E.N. The approximation of linear functionals. SIAM J. Numer. Anal. 3 (1966), 173-182. (MR 36, 589; Zb 147, p. 51; RJM (1967), 7B510.)

2. Atteia, M. * Etude de certains noyaux et theorie des fonctions "spline" en Analyse

Numerique (These). Universite de Grenoble, Grenoble, 1966. (BS ~, 6564.)

3. Atteia, M. Existence et determination des fonctions "spline" a plusieurs variables. C.R. Acad. Sci. Paris Ser. A 262 (1966), 575-578. (MR 33, 3004; Zb 168, p. 350; RJM (1967), 8B478; BS ~, 8613.)

4. Aubin, J.P. * Approximation des espaces de distributions et des operateurs differen­

tiels (These Doct. Sci. Math.). Universite de Paris, Paris, 1966. (BS~, 16561.)

5. Barrodale, I.; Young, A. A note on numerical procedures for approximation by spline functions. Comput. J. 9 (1966), 318-320. (MR 34, 21ST; Zb ]68, p. ]49; RJM (1967), 5B709; CA ll, 69; BS 28, 6535.)

6. Berger, S.A.; Webster, w.e.; Tapia, R.A.; Atkins, D.A. Mathematical ship lofting. J. Ship Research ~ (1966), 203-222.

7. Birkhoff, Go; Boor, C. de; Swartz, B.; Wendroff, B. Rayleigh-Ritz approximation by piecewise cubic polynomials. SIAM J. Numer. Anal. 3 (1966), 188-203. (MR 34, 3773; Zb 144,-p. 380; RJM (1967), 10B681; CA lQ, 3202.)

- 10 - 1966

8. Birman, M.S.; Solomjak, M.Z. (l

Approximation of the functions of the classes Wp by piecewise polynomial functions. Dokl. Akad. Nauk SSSR lL! (1966), 1015-1018 (Russian). Translated as Soviet Math. Dokl. 7 (1966), 1573-1577. ViR 35, 630; RJM (1967), 5BI20; BS-28, 7608.)

9. Boor, C. de * The method of projections as applied to the numerical solution of two

point boundary value problems using cubic splines (Doctoral dissertation). Univ. of Michigan, Ann Arbor, 1966. (BS~, 10097; DA~, 3592-B.)

10. Boor, C. de; Lynch, R.E. On splines and their minimum properties. J. Math. Mech. 15 (1966), 953-969. (MR 34, 3159; Z~185. p. 205.)

II. Carasso, C. * Methodes numeriques pour l'obtention de fonctions-spline (These).

Universite de Grenoble, Grenoble, 1966. (BS 28, 6538.)

12. Ciarlet, P.G. * Variational methods for nonlinear boundary value problems (Doctoral

dissertation). Case Institute of Technology, Cleveland, 1966. (RS ~, 6141; DA~, 2437-B.)

13. Ciesielski, Z. Properties of the orthonormal Franklin system, II. Studia Math. 27 (1966), 289-323. (MR 34, 3202;:Zb 148, p. 47; RJM (1967), 8B75.)

14. Coatmelec, C. Approximation et interpolation des fonctions differentiables de plusieurs . variables. Ann. Sci. Ecole Norm. Sup. 83 (1966), 271-341. (MR38, 469; RJM (1968), IIB94.)

IS. Coatmelec, C. * Approximation et interpolation des fonctions differentiables de plusieurs

variables (These Doct. Sci. Math.). Universite de Rennes, Rennes, 1966. (RJM (1969), 2B135; BS 29, 978.)

16. Curry, H.B.; Schoenberg, I.J. On P6lya frequency functions. IV: The fundamental spline functions and their limits. J. Analyse Math. 17 (1966), 71-107. (MR~, 1884; Zb 146, p. 84; RJM (1967), 11B94; BS 28, 3756.)

17. Ehrich, H. Untersuchungen zur numerischen Fourieranalyse. Math, Z. 91 (1966), 380-420. (MR 34, 7057; RJM (1967), IB466; BS~, 13726.)

- II -

18. Glass, J.M. Smooth-curve interpolation: a generalized spline-fit procedure. BIT 6 (1966), 277-293. (Zb T73, p. 186; RJM (1967), 9B619; CR~, 12801.)

19. Hands comb , D.C. Spline functions.

1966

in: Methods of numerical approximation; ed. by D.C, Handscomb, pp. 163-167. Pergamon Press, Oxford, 1966.

20. Hands comb , D.C. Optimal approximation by means of spline functions. in: Methods of numerical approximation; ed. by D.C. Hands comb , pp, 177-181. Pergamon Press, Oxford, .1966.

21. Hands comb , D. C. Optimal approximation of linear functionals. in: Methods of numerical approximation; ed. by D.C. Handscomb, pp. 169-176. Pergamon Press, Oxford, 1966.

22. Innanen, K.A. An example of precise interpolation with a spline function. J. Computational Phys. I (1966), 303-304. (CR~, 12789; CA Q, 71-:-)

23. Karlin, S.; Studden, W.J. Tchebycheff systems: with applications in analysis and statistics. P? 140-143; pp. 436-454. In~erscience, New York, 1966. (MR 34, 4757; Zb 153, p. 389.)

24. Karlin, S.; Ziegler, Z. Chebyshevian spline functions. SIAM J. Numer. Anal. 3 (1966), 514-543. (MR~, 7041; Zb ~,-p. 310; RJM (1967), 8B603.)

25. Malozemov, V.N. On the deviation of broken lines (Russian, English sunnnary). Ves tnik Leningrad. Dni v. 21 (1966), no. 7, 150-153. (HR 33, 4533; Zb 177, p. 87; RJM (1966), 9B124; BS '!:2, 13]47.)

26. Marsden, M.; Schoenberg, I.J. On variation diminishing spline approximation methods. Mathematica (Cluj) 8 (1966), 61-82. (MR 35, 4648; Zb 17T, p. 310; RJM (1968), 6B142.)

27. Milnes, H.W. A variational approach to smoothing unequally spaced data subject to random errors. Indust. Math. 16 (1966), 77-93. (MR 40, 5108; BS~, 14397.)

28. Schoenberg, I.J. On Hermite-Birkhoff interpolation. J. Math. Anal. Appl. 16 (1966), 538-543. (MR 34, 3160; Zb 156,]p. 287; RJM (1967), 8B598; BS 28, 9344.)

- 12 - 1967

29. Schoenberg, I.J. On lIlonosplines of least squlln' deviation and best quadrature formulae. II. SIA.M J. Nutner. AnHl. J (1%6), 32.)-]28. (HI{ 34,3170; Zb 147,-p. 321; RJM (1967), IIB658.)

30. Schumaker, L.L. * On some approximation problems involving Tchebycheff systems and spline

functions (Doctoral dissertation). Stanford Univ., Stanford, 1966. (RJM (1967), 9B106; BS .?2.., 2535; DA 31., 240-B.)

31. Schweikert, D.G. * The spline in tension (hyperbolic spline) and the reduction of extraneous

inflection points (Doctoral dissertation). Brown Univ., Providence, 1966. (DA 28, 267-B.)

32. Schweikert, D.G. An interpolation curve using a spline in tension. J. Math. and Phys. 45 (1966), 312-317. (MR 34, 6990; Zb 146, p. 141; RJM (1967), 9B617; BS 28, 7843.)

33. Sharma, A.; Meir, A. Degree of approximation of spline interpolation. J. Math. Mech. 15 (1966), 759-767. (MR 33, 3006; Z~158, p. 307; BS 28, 706.)

34. Stern, M.D. * Some problems in the optimal approximation of bounded linear functionals

(Doctoral dissertation). Oxford Univ., Oxford, 1966.

35. Varga, R.S. Hermite interpolation-type Ritz methods for two-point boundary value problems. in: Numerical solution of partial differential equations (Proc. Symp. Univ. Maryland, 1965); ed. by J.H. Bramble, pp. 365-373. Acad. Press, New York, 1966. (MR 34, 5302; Zb ~, p. 357.)

1967

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Complex cubic splines. Trans. Amer. Math. Soc. 129 (1967), 391-413. (MR~, 573; RJM (1968),-gB764; BS.?2.., 11591.)

2. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. * The theory of splines and their applications.

Acad. Press, New York, 1967. (MR 39, 684; Zb 158, p. 159; BS .?2.., 976.)

3. Atteia, M. Sur les fonctions-spline generalisees. in: Actes du 5e Congres de l'AFIRO (Lille, 1966), pp. 113-116. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967.

4. Atteia, M. Fonctions "spline" avec contraintes lineaires de type inegalite. in: Actes du 6e Congres de l'AFIRO (Nancy, 1967), pp. 42-54. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967.

- 13 - 1967

5. Aubin, J.P. Approximation des espaces de distributions et des operateurs differen­tiels. Bull. Soc. Math. France, supplement au numero de Decembre 1967. Memoire no. 12. (RJM (1969), 2B586; BS~, 9570.)

6. Aubin, J. P. Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin's and finite differ­ence methods. Ann. Scuola Norm. Sup. Pisa 4 (1967), 599-637. (RJM (l968), 9B72I; BS~, 12060.)

7. Bel'tjukov, B.A. Approximate solution of integral equations of Volterra type by the method of piece-wise interpolation of the unknown function (Russian). Proc. Sixth Interuniv. Sci. Conf. of the Far East on Phys. and Math., Vol. 3: Differential and Integral Equations, pp. 22-31. Khabarovsk.Gos. Ped. lnst., Khabarovsk, 1967. (MR il, 2959.)

8. Berkovitz, L.D.; Pollard, H. A non-classical variational problem arising from an optimal filter problem. Arch. Rational Mech. Anal. 26 (1967), 281-304. (MR 11, 5994; RJM (1968), 9B386.)

9. Birkhoff, G. Local spline approximation by moments. J. Math. Mech. 16 (1967),987-990. (XR 34, 8051; Z~148, p. 292; RJM (1968), 7B84; BS 28, 13457.)

10. Birkhoff, G.; Priver, A. Hermite interpolation errors for derivatives. J. Math. and Phys. 46 (1967), 440-447. (MR~, 1883; Zb 176, p. 142; RJM (1968), 9B763, BS~, 11982.)

II. Birman, M.S.; Solomjak, M.Z. Piecewise-polynomial approximations of functions of the classes W~. Mat. Sb. 73 (1967), no. 3, 331-355 (Russian). Translate~as Math. USSR-Sb. 2 (1967), 295-318. (HR 36, 576; RJM (1968), 6Bl19; BS 29, 2521.)

12. Carasso, C. Obtention d'une fonction-Spline d'interpolation d'ordre K par une methode d'integration locale. in: Procedures Algol en Analyse Numerique I, pp. 288-291. Centre National de la Recherche Scientifique, Paris, 1967.

13. Carasso, C. Methode pour l'obtention de fonctions-spline d'interpolation d'ordre deux. in: Procedures Algol en Analyse Numerique I, pp. 292-294. Centre National de la Recherche Scientifique, Paris, 1967.

14. Carasso, C. Obtention d'une fonction lisse passant par des points donnes et ayant en ces points des derivees donnees (fonction-spline d'Hermite). ia: Procedures Algol en Analyse Numerique I, 295-299. Centre National de la Recherche Scientifique, Paris, 1967.

- 14 -

15. Car,lsso, C. Obtention de lu d~riv6e d'une fanction donnie par points. in: Prol'cdurL'l'l Algol en Analyse Numerique 1, pp. 300-)01. Centre National de la Recherche scientifique, Paris, 1967.

16. Carasso, C. Construction numerique de fonctions-spline. in: Actes de 5e Congres de l'AFIRO (Lille, 1966), pp. 506-509. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967.

17. Carasso, C. Methode generale de construction de fonctions spline.

1967

Rev. Fran~aise Informat. Recherche Operationnelle 1 (1967), no. 5, 119-127. (MR,R, 667; Zb 163, p. 377; RJM (1968), 10B860; BS 29, 13887.)

18. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S. Numerical methods of high-order accuracy for nonlinear boundary value problems. I: One dimensional problem. Numer. Math. 9 (1967), 394-430. (UR 36, 4813;-Zb 155, p. 204; RJM (1968), 4B751; BS 28, 14094.)

19. Cybertowicz, Z. On some approximation problems. Bull. Acad. Polon. Sci. Sir. Sci. Math. Astronom. Phys. 15 (1967), 497-501. (Zb 176, p. 352; RJM (1968), 6B696; BS ~, 2522.)

20. Ferrand, C. Lissage par utilisation de fonctions analogues aux fonctions spline. in: Actes du 6e Congres de l'AFIRO (Nancy, 1967), pp. 14-31. Assoc. Fran9' d'Inform.et de Rech. Operat., Paris, 1967.

21. Greville,T.N.E. Spline functions, interpolation and numerical quadrature. in: Mathematical methods for digital computers, Vol. II; ed. by A. Ralston and H.S. Wilf, pp. 156-168. Wiley, New York, 1967. (CR i!" 12020.)

22. Greville, T.N.E. On the normalization of the B-splines and the location of the nodes for the case of unequally spaced knots. in: Inequalities I (Proe. Symp. Wright-Patterson Air Force Base, Ohio, 1965); ed. by O. Shisha, pp. 286-291. Acad. Press, New York, 1967. (MR 36, 6848.)

23. Joly, .T.L. Utilisation des fonctions spline pour Ie lissage. in: Actes du 5e Congres de l'AFIRO (Lille, 1966), pp. 349-352. Assoc. Fran~. d'Inform. et de Rech. Operat., Paris, 1967.

24. Joly, J.L. Theoremes de convergence des fonctions spline generales d'interpolation et d'ajustement. C.R. Acad. Sci. Paris Ser. A 264 (1967), 126-]28. (MR l1, 3342; Zb 154, p. 149; RJM (1968), 2B652; BS ~, 9341.)

- 15 - 1967

25. Karlin, S.; Schumaker, L.L. The fundamental theorem of algebra for Tchebycheffian monosplines. J. Analyse Math. 20 (1967), 233-270. (MR 36, 582; Zb 187, p. 20; BS ~, 4264.)

26. Karlin p S.; Ziegler, Z. Chebyshevian spline functions. in: Inequalities I (Proc. Symp. Wright-Patterson Air Force Base, Ohio, 1965); ed. by O. Shisha, pp. 137-149. Acad. Press, New York, 1967. (MR lit 1854; Zb 1LL, p. 310; RJM (1969), 5B925.)

27. Loscalzo, F.R.; Talbot, T.D. Spline function approximations for solutions of ordinary differential equations. Bull. Amer. Math. Soc. 73 (1967), 438-442. (MR~, 1218; Zb 1LL, p-.-363; BS ~, 4318.)

28. Loscalzo, F.R.; Talbot, T.D. Spline function approximations for solutions of ordinary differential equations. SIAM J. Numer. Anal. 4 (1967), 433-445. (MR 36, 4808; Zb 1LL,-p. 363; RJM (1971), 3B588; CA ll, 90; BS 29, 10044.)

29. Malozemov, V.N. Polygonal interpolation. Mat. Zametki I (1967), 537-540 (Russian). Translated as-Math. Notes I (1967), 355-357. (MR 35, 5816; RJM (1968), TB145; BS 28, 13482.)

30. Meinguet, J. Optimal approximation and error bounds in seminormed spaces. Numer. Math. 10 (1967), 370-388. (MR 1I, 6012;~JM (1968), 9B790; CA l!, 878; BS ~, 11991.)

31. Nord, S. Approximation properties of the spline fit. BIT 7 (1967), 132- 1 44. (MR 36, 1887; Zb 1LL, p. 373; RJM (1968), 5B820; CA ll, 2215.)

32. Perrin, F.M. * &1 application of monotone operators to differential and partial differ­

ential equations on iftfinite domains (Doctoral dissertation). Case Institute of Technology, Cleveland, 1967.

33. Reinsch, C.H. Smoothing by spline functions. Numer. Math. 10 (1967), 177-183. (Zb ~, p. 362; RJM (1968), 6B850; CR~, 14528; BS ~, 8230.)

34. Rice, J.R. Characterization of Chebyshev approximations by splines. SIAM J. Numer. Anal. 4 (1967), 557-565. (MR 36,6851; Zb 187,-p. 329; BS 29, 11993.)

35. Sard, A. Optimal approximation. J. Functional Analysis (1967), 222-244. (MR 36,3037; Zb 158, p. 136.)

- 16 - 1968

36. Schoenberg, I.J. On spline functions. in: Inequalities I (Proe. Symp. Wright-Patterson Air Force Base~ Ohio, 1965); ed. by O. Shisha, pp. 255-286. Acad. Press, New York, 1967. (MR 36, 6848; RJM (1969), 5B926.)

37. Schultz, M.H.; Varga, R.S. L-splines. Numer. Math. 10 (1967), 345-369. (MR E.., 665; Zb 183, p. 444; RJM (1968), 6B842; CA.,!l, 872; BS l2., 11995.)

38. Smoluk., A. On piecewise approximation of functions (Polish). Prace Nauk Wyzszej Szkoly Ekon. Wroclawiu (1967), no. 6, 101-)08. (RJM (1968), IB776.)

39. Smoluk, A. Examples of piecewise approximation of functions (Polish). Prace Nauk Wyzszej Szkoly Ekon. Wroclawiu (1967), no. 6, 109-126. (RJM (1968), IB775.)

40. Stern, M.D. Optimal quadrature formulae. Comput. J. 9 (1967), 396-403. (MR 35, 3885; RJM (1969), 8B748; CA ll' 836; BS 28, 10880.)

41. Subbotin, Yu.N. Piecewise polynomial (spline) interpolation. Mat. Zametki 1 (1967), 63-70 (Russian). Translated as-Math. Notes I (1967), 41-45. (MR~, 4645; Zb 159, p. 84; RJM (1967), 10B142; BS 28, 11774.)

42. Subbotin, Yu.N. Interpolation by functions with nth derivative of minimum norm. Trudy Mat. lnst. Steklov 88 (1967). 30-60 (Russian). Translated as Approximation of functions in the mean;ed. by S.B. Steckin (Proc. Steklov Inst. Math. 88 (1967»,pp. 31-63. Amer. Math. Soc., Providence, 1969. --(RJM (1968), 8B93; BS ~, 4270.)

43. Young, J.D. Numerical applications of cubic spline functions. The Logistics Review 3 (1967), no. 14, 9-14. (RJM (1968), IOB861; CR ll, 19816.)

1968

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Cubic splines on the real line. J. Approximation Theory 1 (1968), 5-)0. (MR 37, 6650; Zb 179, p.-365.)

2. Ahuja, D.V. An algorithm for generating spline-like curves. IBM Systems J. 7 (1968), 206-217.

- 17 -

3. Ahuja, D.V.; Coons, S.A. Geometry for construction and display. IBM Systems J. l (1968), 188-205.

4. Amunrud, L.R.

1968

* Tchebycheff approximations by general spline functions (Doctoral disser­tation) . Montana State Univ., Montana, 1968. (DA~, 4254-B.)

5. Anselone, P.M.; Laurent, P.J. A general method for the construction of interpolating or smoothing spline-functions. Numer. Math. 12 (1968), 66-82. (11R 40, 3145;:Zb 197, p. 135; RJM (1969), 2B838; CA ll, 55; BS 30, 5050.)

6. Atkinson, K.E. On the order of convergence of natural cubic spline interpolation. SIAM J. Numer. Anal. 5 (1968), 89-101. (MR 37, 1853; Zb 208,-p. 408; RJM (1971), 4BI000j CR..!..!., 18292; BS 29, 17087.) -

7. Atteia, M. Fonctions "spline" definies sur un ensemble convexe. Numer. Math. 12 (1968), 192-210. (MR 41, 2265;:Zb 186, p. 452; RJM (1969), 4B659; CR~, 21056; BS 30, 6605.) -

8. Aubin, J.P. Interpolation et approximation optimales et "spline functions ll

•

J. Math. Anal. Appl. 24 (1968), 1-24. (MR 37, 6651; RJM (1969), 7BI02; BS 30, 6358.)

9. Aubin p J.P. Best approximation of linear operators in Hilbert spaces. SIAM J. Numer. Anal. 5 (1968), 518-521. (MR 38, 6743; Zb 176,-p. 131; RJM (1971), 3B434; BS 30, 12694.)

10. Bickley, W.G. Piecewise cubic interpolation and two-point boundary problems. Comput. J •. II (1968),206-208. (MR 37, 6036; Zb 155, p. 480; RJM (1969), 2B790; CA~, 2551; BS 30, 5010.) -

11. Birkhoff, G.; Schultz, M.H.; Varga, R.S. Piecewise Hermite interpolation in one and two variables with appplica­tions to partial differential equations. Numer. Math. 11 (1968), 232-256. (MR 37, 2404;:Zb 159, p. 209; RJM (1968), 11B732; CA~, 2291; BS 29, 17158.) -

12. Birkhoff, G.; Gordon, W.J. The draftsman's and related equations. J. Approximation Theory ~ (1968), 199-208. (MR 38, 4055.)

J 3. Boor, C. de On local spline approximation by moments. J. Math. Mech. 17 (1968), 729-735. (MR 36, 6850; Z~162, p. 84.)

- 18 -

14. Boor, C. de On the convergence of odd-degree spline interpolation. J. Approximation Theory I (1968). 452-463. (MR 38, 6273; Zb 174, p.-99.)

15. Boor, C. de On aniform approximation by splines. J. Approximation Theory I (1968), 219-235. (UR l2.., 1866; Zb 193, p.-25.)

16. Buchanan, J.E.; Thomas, D.H.

1968

On least-squares fitting of two-dimensional data with a special structure. SIAM J. Numer. Anal. 5 (1968), 252-257. (MR 1I, 3740; RJM (1971), 4BIOI2; BS ~, 4929.)

17. Bulirscb, R.; Rutishauser, H. Spline-Interpolation. in: Mathematische Hilfsmittel des Ingenieurs, Vol. 3; hrsg. von R. Sauer und I. Szabo, pp. 265-277. Springer Verlag, Berlin, 1968. (MR 1I, 71 IS; Zb 193, p. 352.)

18. Cavendish, J.C.; Price, H.S.; Varga, R.S. Numerical methods of higher-order accuracy for diffusion-convection equations. Soc. Petroleum Engrs. AlME J. ~ (1968), 293-303.

19. Cheney, E.W.; Schurer, F. A note on the operators arising in spline approximation. J. Approximation Theory I (1968), 94-102. (MR 1I, 5580; Zb 177, p.-89.)

20. Cherruault, Y. * Approximation d'operateurs lineaires et applications (These).

(Monographies d'Informatique, Vol. 4). Dunod, Paris, 1968. (MR 38, 4879; Zb 169, p. 196; RJM (1969), 5B909; BS 29, 16864.)

21. Ciarlet, P.G. AIL 0(h2) method for a non-smooth boundary value problem. Aequationes Math. 2 (1968), 39-49. (MR 38, 869; Zb 159, p. 117; RJM (1969), 2B794; BS 30, 14610.)

22. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S. Numerical methods of high-order accuracy for nonlinear boundary value problems. II: Nonlinear boundary conditions. Numer. Math. 11 (1968), 331-345. (MF. 37, 4965jZb 176, p. 149; RJM (1968), 12B769; CA g, 2548; BS 30, 2368.) -

23. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S. Numerical methods of high-order accuracy for nonlinear boundary value p~oblems. III: Eigenvalue problems. Numer. Math. 12 (1968), 120-133. (XR 38, 1838; J£!., p. 183; RJM (1969), IB746; CA 11, 277; BS 30, 5023.)

24. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S. Numerical methods of high-order accuracy for nonlinear boundary value problems. IV: Periodic boundary conditions. Numer. Math. 12 (1968), 266-279. (HR 39, 2337;Zb 181, p. 183; RJM (1969), 4B609; CR.!.!.., 19297; BS 30, 10923.) -

- 19 - 1968

25. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S. Numerical methods of high-order accuracy for nonlinear two-point boundary value problems. in: Programmation en Mathematique Numerique (ColI. Intern. CNRS, no. 165, Besan~on, 1966), pp. 217-22S. Centre National de la Recherche Scientifique, Paris, 1968. (MR 38, 1837; Zb 207, p. 164; RJM (1968), 12B768; BS~, 17160.)

26. Ciesielski, Z. A bounded orthonormal system of polygonals. Studia Math. 31 (1968), 339-346. (MR 38, 3686;:Zb 169, p. 402; RJM (1969), 9B83.)

27. Cybertowicz, Z. On some approximation problems. Frace Mat. 12 (1968), 61-74. (MR 38, 2496; RJM (1969), SB76S; BS 30, 8117.)

28. Diring~r, P.

29.

Interpolation, derivation et integration a. l'aide de fonctions spline. Recherche Aerospat. 124 (1968), 13-16. (RJM (1969), 2B841; BS 30, S046.)

Ducateau, Ch.F. Condition pour l'interpolation par des fonctions de Hk[a,SJ sur un nombre infini de points. C.R. Acad. Sci. Paris Ser A 267 (1968), 309-312. (MR 40, 4652; RJM (1969), SB642.)

30. Einarsson, B. Numerical calculation of Fourier integrals with cubic splines. BIT 8 (1968), 279-286. (MR 39, 1114; Zb 187, p. 105; RJM (1969), 9BS69; CR!Q, 17886; CA~, 542.)

31. El Tom~ M.E.A. * Numerical approximation of functions of one or more variables (Doctoral

dissertation). Oxford Univ., Oxford, 1968.

32. Fix, G. * Bounds and approximations for eigenvalues of self-adjoint boundary value

problems (Doctoral dissertation). Harvard Univ., Cambridge (Mass.), 1968.

33. Forrest, A.R. * Curves and surfaces for computer aided design (Doctoral dissertation).

Cambridge Univ., Cambridge, 1968.

34. Golomb, M. Approximation by periodic spline interpolants on uniform meshes. J. Approximation Theory 1 (1968), 26-6S. (MR 38, 1444; Zb 18S, p.-309.)

35. Hall, C.A. . On error bounds for spline interpolation.

J. Approximation Theory 1 (1968), 209-218. (MR 39, 681; Zb 177, p. 89.)

- 20 - 1968

36. Herbold, R.J. * Consistent quadrature schemes for the numerical solution of boundary

value problems by variational techniques (Doctoral dissertation). Case Western Reserve Univ., Cleveland, 1968. (CR,2., 15006; DA 30, 165-B.)

37. Horsley, A.; Parker, J.B.; Parker, K.; Price, J.A. Curve fitting and statistical techniques for use in the mechanized evaluation of neutron cross sections. Nuclear Instruments and Methods ~ (1968), 29-42.

38. Hulme~ B.L. Interpolation by Ritz approximation. J. Math. Mech. 18 (1968), 337-341. (MR 1I, 7090; Z~165, p. 386; RJM (1969), 10B627; BS 30, 9852.)

39. Ikaunieks, ~.A.; Ermuta, A.E. Concave piecewise-polynomial interpolation (Russian; Latvian and English sunnnaries). in: Latvian Math. Yearbook, Vol. 4, pp. 149-163. 17.dat. "Zinatne", Riga, 1968. (MR~, 2293; Zb 208, p. 409.)

40. Jerome, J.W.; Schumaker, L.L. A note on obtaining- natural spline functions by the abstract approach of Atteia and Laurent. SIAM J. Numer. Anal. 5 (1968), 657-663. (MR 40, 6127; Zb 185,-p. 409; RJM (1971), 4BI001; BS 30, 14544.)

41. Johnson, a.G. * Convergence, error bounds, sensitivity, and numerical comparisons of

certain absolutely continuous Rayleigh-Ritz methods for Sturm-Liouville eigenvalue problems (Doctoral dissertation). Univ.of California, Berkeley, 1968. (DA~, 3396-B.)

42. Karlin, S. 'Cotal positivity, Vol. }. pp. 357-364; pp. 501-564. Stanford Univ. Press, Stanford, 1968. (MR 1I, S667; RJM (1969), SB651.)

43. Karlir., S.; Karon, J.M. A variation-diminishing generalized spline approximation method. J. Approximation Theory 1 (1968), 255-268. (MR 38, 3664; Zb 165, p.-386.)

44. Karon, J.M. * The sign-regularity properties of a class of Green's functions for

ord.inary differential equations and some related results (Doctoral dissertation). Stanford Univ., Stanford, 1968. (RJM (1969), 12B300; DA~, 2529-B.)

45. Lauren~, P.J. Representation de donnees experimentales a l'aide de fonctions-spline d'ajustement et evaluation optimale de fonctionnelles lineaires conti­nues. ApI. Mat. 13 (1968),154-162. (MR 38, 4000; Zb 155, p. 219; RJM (1968), 12B849; BS 30, 2209.)

- 21 -

46. Laurent, P.J. Theoremes de characterisation en approximation convexe. Mathematica (Cluj) 10 (1968), 95-111. (MR i!,., 70 1; RJM (1969), JOV302; BS 30, 4581.)

47. Loscalzo, F.R.

1968

* On the use of spline functions for the numerical solution of ordinary differential equations (Doctoral dissertation). Univ. of Wisconsin, Madison, 1968. (DA 29, 2983-B.)

48~ Marsden, M.J. * An identity for spline functions with applications to variation-dimin­

ishing spline approximation (Doctoral dissertation). Univ. of Wisconsin, Madison, 1968. (DA 29, 2985-B.)

49. Meir, A.; Sharma, A. One-sided spline approximation. Studia Sci. Math. Hungar. 3 (1968), 211-218. (MR 38, 1445; Zb 175, p. 350; RJM (1969), 6B151; BS 30, 6601.)

50. Meir, A.; Sharma, A. Convergence of a class of interpolatory splines. J. Approximation Theory I (1968), 243-250. (MR 38, 3665; Zb 186, p.-114.)

51. Munteanu, M.J. Observations on the optimal solution of a nonlinear differential boundary value problem in the subspace of generalized spline functions (Roumanian). Bul. sti. lnst. Politehn. Cluj 11 (1968), 47-56. (MR 40, 7522.) --

52. Ostapenko, V.N.; Khazankina, N.P. On a method to approximate signals (Russian). Avtomatika (Kiev) ~ (1968), 75-80.

53. Phillips, G.M. Algorithms for piecewise straight line approximations. Comput. J. ] 1 (1968), 21 ]-212. (MR 37, 6013; Zb 165, p. 512; RJM (1969), IB792; CA g, 2529; BS 30, 4927.)

54. Powell, M.J.D. On best L2 spline approximations. in: Numerische Mathematik, Differentialgleichungen, Approximationstheorie (Proc. Conf. Oberwolfach, 1966); hrsg. von L. Collatz, G. Meinardus und H. Unger, pp. 317-339. Birkhauser Verlag, Basel, 1968. (MR 42, 2631; BS 30, 6604.)

55. Sard, A. Optimal approximation: an addendum. J. Functional Analysis 2 (1968), 368-369. (MR 38, 1457; Zb ]59, p7 438; RJM (1969), 6B721; BS 30, 4584.)

56. Schoenberg, I.J. On the Ahlberg-Nilson extension of spline interpolation: the g-splines and their optimal properties. J. Math. Anal. Appl. 21 (1968), 207-231. (MR 36, 6849; Zb 159,-p. 84; RJM (1968), 7B728; BS 29, 11996.)

- 22 -

57. Schoenberg, I.J. On'spline interpolation at all integer points of the real axis. M~thematica (Cluj) 10 (1968), 151-170. (~IR 38,6274; Zb 183, p. 331; RJM (1969), 7B101; BS 30,4578.)

58. Schoenberg, I.J. Spline interpolation and the higher derivatives.

1968

in~ Abhandlungen aus Zahlentheorie und Analysis; hrsg. von P. Turin, pp. 279-295. Deutscher Verlag der Wissenschaften, Berlin, 1968. (ZbI98, p. 90.)

59. Schumaker, L.L. Uniform approximation by Tchebycheffian spline functions. J. Math. Mech. 18 (1968), 369-377. (MR 39, 3203; Z~165, p. 386; RJM (1969), 12B146; BS 30, 8110.)

60. Schumaker, L.L. Uniform approximation by Chebyshev spline functions. II: Free knots. SIAM J. Numer. Anal. 5 (1968), 647-656. (MR 39, 3204; Zb 169,-p. 394; BS 30, 14545.)

61. Schurer, F. A note on interpolating periodic quintic splines with equally spaced nodes. J. Approximation Theory 1 (1968), 493-500. (MR 38, 6275; Zb 186, p. 14.)

62. Schurer., F.; Cheney, E.W. On interpolating cubic splines with equally-spaced nodes. Nederl. Akad. Wetensch. Proc. Ser. A 71 (1968), 517-524. (MR 40,6129; Zb 184, p. 379; RJM (1969), 10B113; CR 12, 21413; BS 30, 9851.) - -

63. Shisha, O. Trends in approximation theory. Appl. Mech. Rev. 21 (1968), 337-341. (RJM (1969), IB797; BS 30, 2197.)

64. Simpson, R.B. Approximation of the minimizing element for a class of functionals. SIAM J. Numer. Anal. 5 (1968), 26-41. (MR 1I, 3414; RJM (1971), 3B522; CA~, 1956; BS 29, 17096.)

65. Smirnov, V.M. A method for the smooth interpolation of functions. Z. Vy~isl. Mat. i Mat. Fiz. 8 (1968), 1330-1331 (Russian). Translated as USSR Comput. Math. and Math. Phys. 8 (1968), no. 6, 190-193. (MR~, 5839; Zb 206, p. 467; RJM (1969), 4B662; is 30, 10861.)

66. Spath, H. Ein Verfahren zur flachentreuen Approximation von Treppenfunktionen durch glatte Kurven. Z. Angew. Math. Mech. 48 (1968), TI06-TI07. (RJM (1969), IOB676; BS30, 18375.)

67. Swartz. B. O'(h2n+2-x,) bounds on some spline interpolation errors. Bull. Amer. Math. Soc. 74 (1968), 1072-1078. (MR 38, 4869; Zb ~, p--. 340; BS 30, 8124.)

- 23 - 1969

68. Van Armau, D.J. * Classification of experimental designs relative to polynomial spline

regression functions (Doctoral dissertation). Purdue Univ., Lafayette, 1968. (DA 29, 3967-B.)

69. Young, J.D. Numerical applications of hyperbolic spline functions. The Logistics Review 4 (1968), no. 19, 17-22. (RJM (1969), 7B659; CR ll, 19817.)

70. Young, J.D. Numerical applications of damped cubic spline functions. The Logistics Review 4 (1968), no. 20, 33-37. (RJM (1969), IOB677; CR ll, 19818.)

1969

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Properties of analytic splines. I: Complex polynomial splines. J. Math. Anal. Appl. 27 (1969), 262-278. (MR~, 8136; Zb 185,])'. 135; RJM (1970), 2B209; BS 1..!., 3145.)

2. Ahlberg, J.H. Splines in the complex plane. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. )-27. Acad. Press, New York, 1969. (MR~, 2264.)

3. Albasiny, E.L.; Hoskins, W.D. Cubic spline solutions to two-point boundary value problems. Comput. J. 12 (1969), 151-153. (MR 39, 3710; Zb 185, p. 414; RJM (1969), 12B825; CR ll, 18302; CA 13 , 3112; BS 31, 1368.)

4. Amos, D.E.; Slater, M.L. Polynomial and spline approximation by quadratic programming. Comma ACM 12 (1969), 379-381. (MR 43, 5681; Zb 187, p. 127; RJM (1970), 3B873; CA 11, 2422; BS 1..!., 7789.)

5. Barnhill, R.E.; Wixom, J.A. An error analysis for the bivariate interpolation of analytic functions. SIAM J. Numer. Anal. 6 (1969), 450-457. (~~ 43, 5683; Zb 187,-p. 501; CR~, 21058; BS 1..!., 13242.)

6. Bedau, X.D. Darstellung und Fortschreibung von Einkommensschichtungen unter Verwen­dung von Spline-Funktionen. Viertelj ahrshefte zur Wirtschaftsforschung (1969), 406-425. (RJM (1970), 11B864.)

7. Bellman, R.; Roth, R. Curve fitting by segmented straight lines. J. Amer. Statist. Assoc. 64 (1969), 1079-1084. (MR~, 7760; RJM (1970),-SB780; BS 1..!., 12212.)

8. Berkovitz, L.D.; Pollard, H. A variational problem related to an optimal filter problem with self­correlated noise. Trans. Amer. Math. Soc. 142 (1969), 153-175. (MR 39, 7484.)

- 24 - 1969

9. Bhattacharyyu, B.K. H;cubic spline interpolation IlH It method lor treatment of potential fidd dutll. GeophysicB 34 (1969), 402-423.

10. Bickley, W.G. Piecewise cubic interpolation and two-point boundary problems. (Letter to the editor.) Comput. J. 12 (1969),105. (CA Q, 278"'9:")

II. Birkhoff, G. Numerical solution of elliptic equations. in: Lecture series 1n differential equations, Vol. 2; ed. by A.K. Aziz; pp. 197-232. Van Nostrand Reinhold Company, New York, 1969. (Zb 208, p. 192.)

12. Birkhoff, G. Piecewise bicubic interpolation and approximations in polygons. in: Approximations with special emphasis on spline functions; ed. hy I.J. Schoenberg, pp. 185-221. Acad. Press, New York, 1969. (MR~, 6469.)

13. Blue, J.L. Spline function methods for nonlinear boundary-value problems. Comm. ACM 12 (1969), 327-330. (MR 44, 1225; Zb 175, p. 161; RJM (1969), 12B823; CR..!.Q., 17706; CA 13, 2032; BS 31, 3179.)

14. Boor, C. de On the approximation by y-polynomials. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 157-183. Acad. Press, New York, 1969. (MR iL, 4096.)

15. Carasso, C.; Laurent, P.J. On the numerical construction and the practical use of interpolating spline functions. in: Information Processing 68 (Proc. IFIP Congress, Edinburg, 1968); ed. by A.J.H. Morrell, Vol. 1 - Mathematics, Software, pp. 86-89. North-Holland Publ. Co., Amsterdam, 1969. (MR 40, 8219; Zb ~, p. 449; CA~, 1477.)

16. Cavendish, J.C.; Price, H.S.; Varga, R.S. Galerkin methods for the numerical solution of boundary value problems. Soc. Petroleum Engrs.AlME J. 9 (1969), 204-220. (BS 1l, 3502.) -

17. Ciarlet, P.G.; Schultz, M.H.; Varga, R.S. N~merical methods of high-order accuracy for nonlinear boundary value problems. V: Monotone operator theory. Nl'mer. Math. 13 (1969),51-77. (MR 40, 3730;Zb .!!L, p. 186; RJM (1969), IOB654; CA Q, 2420; BS }O, 18488.)

18.

- 25 -

Ciesielski, Z. (I) 2 A construction of basis in C (I). Stadia Math. 33 (1969), 243-247. (MR 40, 1759;zh 185, p. 376; BS l,!.,

1969

4710.)

19. Dailey, J.W. * Approximation by spline-type functions and related problems (Doctoral

dissertation) • Case Western Reserve Univ., Cleveland, 1969. (DA l,!., 3537-B.)

·20. Denmar~, H.H.; Larkin, W. J. Invariance conditions on ordinary differential equations defining smooth­ing functions. SIAM J. Appl. Math. ~ (1969), 1246-1257. (MR i!., 685.)

21. Einarsson, B. Erratum to: Numerical calculation of Fourier integrals with cubic splines. BIT! (1969), 183-184.

22. Elhay, S. Optimal quadrature. Bull. Austral. Math. Soc. I (1969), 81-108. (MR i!., 2925; Zb 175, p. 351; RJM (1970), 5B772; BS l,!., 15862.)

23. Esch, ~.E.; Eastman, W.L. Computational methods for best spline function approximation. J. Approximation Theory 2 (1969), 85-96. (MR 39, 1867; Zb ~, p.-176; RJM (1970), IB8IS.)

24. Fitzgerald, C.H.; Schumaker, L.L. A differential equation approach to interpolation at extremal points. J. Analyse Math. 22 (1969), 117-134. (MR i!., 2257; BS 31, 15430.)

25. Fix, G. Higher-order Rayleigh-Ritz approximations. J. Math. Mech. 18 (J969), 645-657. (MR 39, 2349; Zb234 , 65095; RJM (1969), IOB636; BS 30, 16414.)

26. Fix, G.; Strang, G. Fourier analysis of the finite element method in Ritz-Galerkin theory. Studies in Appl. Math. 48 (1969), 265-273. (MR i!., 2944; Zb 179, p-. 225; RJM (1970), 4B874; BS l,!., 9902.)

27. Freeman, H.; Glass, J.M. On the quantization of line-drawing data. IEEE Trans. Systems Sci. Cybernetics SSC-5 (1969), 70-79. (RJM (1969), 12V564.)

28. Fyfe, D.J. The use of cubic splines in the solution of two-point boundary value problems. Comput. J. 12 (1969), 188-192. (MR 39 5065; Zb 185, p. 414; RJM (1969), 12B824; CR!l, 18303; CA _1_, 3137; BS l,!., 1310.)

- 26 - 1969

29. Golomb, M. Spline interpolation near discontinuities. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg. pp. 51-74. Acad. Press, New York, 1969. (MR i!., 693.)

30. Gordon, W.J. Distributive lattices and the approximation of multivariate functions. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 223-277. Acad. Press, New York, 1969. (MR 43, 77 9 • )

31. Gordon, W.J. Spline-blended surface interpolation through curve networks. J. Math. Mech. 18 (1969), 931-952. (~1R 1.2.. 7333; Zb192, p. 422; RJM (1970), 2B963; BS lL. S03.)

32. Greville, T.N.E. * Theory and applications of spline functions (Proc. Seminar Math. Res.

Center, Univ. Wisconsin, Oct. 1968); ed. by T.N.E. Greville. Acad. Press, New York, 1969. (¥~ 38. 3663; BS 33, 3567.)

33. Greville, T.N.E. Introduction to spline functions. in: Theory and applications of spline functions; ed. by T.N.E. Greville, pp. 1-35. Acad. Press, New York, 1969. (~lR 1.2., 186S; Zb 215, p. 176.)

34. Guglielmo, F. di Construction d'approximations des espaces de Sobolev sur des reseaux en simplexes. Calcolo ~ (1969), 279-331.

35. Hall, C.A. Error bounds for periodic quintic splines. Corum. ACM 12 (1969), 450-452. (MR 43, 5685; Zb 185, p. 408; RJM (1970), 3B871; CR 11, 18293; CA 13, 2778; BS 31, 7762.)

36. Hall, C.A. Bicubic interpolation over triangles. J. Math. Mech. 19 (1969), )-11. (MR 39, 6523; Zb194, p. 471; BS lL, 9893.)

37. Heindl, G. Spline-Funktionen mehrerer Veranderlicher. I: Definition und Erzeugung durch Integration. Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B. (1969), 49-63. (Zb 221, 41012; RJM (1971), 3BS6; BS 32, 5690.)

3S. Herbold, R.J.; Schultz, M.H.; Varga, R.S. The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques. Aequationes Math. 3 (1969), 247-270. (MR i!., 6410; Zb 196, p. 176; RJM (197]), 6BS78; BS ~, 510.)

- 27 - 1969

39. Herbold, R.J.; Schultz, M.H.; Varga, R.S. The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques. Aequationes Math. l (1969), 197-198.

40. Hilbert p S.R. * Num~rical methods for elliptic boundary problems (Doctoral dissertation).

Univ. of Maryland, College Park, 1969. (DA~, 1399-B.)

4 I. Hill, LD. Note on algoritm 40: Spline interpolation of degree three. Comput. J. ~ (1969), 409.

42. Hosaka~ M. Theory of curve and surface synthesis and their smooth fitting. Information Processing in Japan 9 (1969), 60-68. (MR il, 9422.) -

43. Hulme, B. L. * Pi~cewise bicubic methods for plate bending problems (Doctoral disser­

tation). Harvard Univ., Cambridge (Mass.), 1969.

44. Jerome, .J.W.; Varga, R.S. Gen~ralizations of spline functions and applications to nonlinear boundary value and eigenvalue problems. in: Theory and applications of spline functions; ed. by T.N.E. Greville, pp. 103-155. Acad. Press, New York, 1969. (MR 39, 685; Zb 188, p. 130.)

45. Jerome, J.W.; Schumaker, L.L. On Lg-splines. J. Approximation Theory 2 (1969), 29-49. (MR 1!, 3201; Zb 172, p.-345; RJM (1970), IB 817.)

46. Jerome, J.W.; Schumaker, L.L. Characterizations of functions with higher order derivatives in Lp' Trans. Amer. Math. Soc. 143 (1969), 363-371. (MR il, 8600; Zb 187, p.-Y]7; BS~, 11303.)

47. Johnson,' O.G. Error bounds for Sturm-Liouville eigenvalue approximations by several piecewise cubic Rayleigh-Ritz methods. SIAM J. Numer. Anal. 6 (1969), 317-333. (MR 41, 4789; Zb 183,-p. 446; RJM (1970), 5B732; CR!!, 19634; as 3 I , I 3288. ) -

48. Karlin, S. Best quadrature formulas and interpolation by splines satisfying bound­ary conditions. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 447-466. Acad. Press, New York, 1969. (MR il, 2275.)

49.

50.

51.

52.

- 28 - 1969

Karlin, S. The fundamental theorem of algebra for monosplines satisfying certain boundary conditions and applications to optimal quadrature formulas. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 467-484. Acad. Press, New York, 1969. (MR~, 2276.)

Karon, .T.M. The sign-regularity properties of a class of Green's functions for ordinary differential equations. J. Differential Equations 6 (1969), 484-502. (MR~, 3863; BSi!., 5127.) .

Kershaw! D. The explicit inverses of two commonly occurring matrices. Muth. Compo 23 (1969), 189-191. (MR 38, 6754;-RJM (1969), IIA313; BS 30, 16385.) '0/'// " v Korne1cuk, N.P.; Luspa1, N.E. Besc quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation. Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 1416-1437 (Russian). Translated as Math. USSR-Izv. 3--(1969), 1335-1355. (MR 43, 4249; Zb 198, p. 89; BS i!., 9377.)

53. Krinzesza, F. * Zur periodischen Spline-Interpolation (Dissertation).

Ruh~-Universitat, Bochum, 1969. (RJM (1971), 8B72.)

54. Lathrop, J.F. * AFplication of spline functions to the numerical solution of ordinary

and partial differential equations (Doctoral dissertation). Univ. of Colorado, Boulder, 1969. (DA 30, 4701-B.)

55. Laurent, .P.J. Construction of spline functions in a convex set. in: Approximations with special emphasis on spline functions; ed. by 1. J. Schoenberg, pp. 415-446. Acad. Press, New York, J969. (MR 40, 6147.)

56. Lee, J.W. * The study of a class of boundary value problems with cyclic totally

positive Green's functions with applications to spline approximation and eigenvalue problems (Doctoral dissertation). Stanford Univ., Stanford, 1969. (DA 30, 1244-B.)

57. Logincv, A.S. Approximation of continuous functions by broken lines. I

Mat. Zametki 6 (1969), 149-160 (Russian). Translated as-Math. Notes 6 (1969), 549-555. (~tR~, 687; Zb 177, p. 88; BS ll, 5102.)

- 29 - 1969

58. Loscalzo, F.R. An introduction to the application of spline functions to initial value problems • in: Theory and applications of spline functions; ed. by T.N.E. Greville, pp. 37-64. Acad. Press, New York, 1969. (MR 39, 2334; Zb ~, p. 165.)

59. Mangas&rian, O.L.; Schumaker, L.L. Splines via optimal control. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 119-156. Acad. Press, New York, 1969. (MR!:J,., 4073.)

60. Mansfield, L.E. * Optimal approximation and error bounds in spaces of multivariate func­

tions (Doctoral dissertation). Univ. of Utah, Salt Lake City, 1969. (DA 30, 2298-B.)

61. Maruashvili, T.I. Th~ best approximation of continuous functions by piecewise linear functions. Trudy Vy~isl. Centra Akad. Nauk Gruzin. SSR. (1969), no. 1, 13-28.

62. Mehlum, E. * Curve and surface fitting based on variational criteria for smoothness

(Doctoral dissertation). Central Inst. for Industrial Research, Oslo, 1969.

63. Meir, A.; Sharma, A. Or. uniform approximation by cubic splines. J. Approximation Theory 2 (1969), 270-274. (HR 40,3137; Zb 183, p.-330; RJM (1970), 2B957; BS~, 813.)

64. Morin, M. * Methodes de calcul des fonctions "spline" dans un convexe (These).

Universite de Grenoble, Grenoble, 1969. (RJM (1972), 1B1235; BS ll, 17640.)

65. Murty, V.N. * Optimal designs of individual regression coefficients with a

Tchebycheffian spline regression function (Doctoral dissertation). Purdue Univ., Lafayette, 1969. (DA 30, 5283-B.)

66. Natterer, F. Numerische Behandlung singularer Sturm-Liouville-Probleme. Numer. Math. 13 (1969), 434-447. (MR 40, 5143;:Zb 182, p. 497; RJM (1970), 3B801; CR ll, 19281; BS 31, 13344.) -

67. Nitsche, J. Satze vom Jackson-Bernstein-Typ fur die Approximation mit Spline­Funktionen. Math. Z. 109 (1969), 97-106. (~~~, 4567; Zb 174, p. 355; BS 30, 17891.)

- 30 -

68. Nitsche, J. Orthogonalreihenentwicklung nach li nearen Spline-Funkt1onen. J. Approximation Theory 2 (1969), 66-78. (i1R 40, 4653; Zb 174, p.-360; RJM (1970), 2B962.)

69. Nitsche, J. Umkehrsatze fur Spline-Approximationen. Compositio Math. 21 (1969), 400-416. (MR iL, 4074; Zb 199, p. 393; BS ~, 20278.)

70. Nitsche, J. Eine Bemerkung zur kubischen Spline-Interpolation.

1969

in: Abstract spaces and approximation (Proc. Conf. Oberwolfach, 1968); ed. by P.L. Butzer and B.S. Nagy, pp. 367-372. Birkhauser Verlag, Basel, 1969. (HR iL, 7344; Zb 202, p. 158; BS ~, 9425.)

71. Nitsche, J. Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville­Randwertproblemen. Numer. Math. 13 (1969), 260-265. (MR 43, 4262;Zb~, p. 182; CR l,!., 18291; BS~, 7786.)

72. Ostapenko, V.N.; Khazankina, N.P. Piecewise polynomial functions and their applications in the algorithmi­zation of electrotechnical calculations (Russian). Nekotor. Vopr. Prikl. Mat. (Kiev) 4 (1969), 268-274. (RJM (1970), 10B789.) -

73. Perrin, F.M.; Price, H.S.; Varga, R.S. On higher-order numerical methods for nonlinear two-point boundary value problems. Numer. Math. 13 (1969),180-198. (MR 40, 8276;:Zb 183, p. 445; RJM (1969), 11B673; CR ll, ]8703; BS 3] , 3 135 • ) -

74. Pierce, J.G. * Higher order convergence results for the Rayleigh-Ritz method applied

to a special class of eigenvalue problems (Doctoral dissertation). Case Western Reserve Univ., Cleveland, 1969. (DA 30, 4264-B.)

75. Powell, M.J.D. A comparison of spline approximations with classical interpolation methods. in: Information Processing 68 (Proc. IFIP Congress, Edinburg, 1968); ed. by A.J.H. Morrell, Vol. 1 - Mathematics, Software, pp. 95-98. Noeth-Ho1land Publ. Co., Amsterdam, 1969. (MR 40,8223; Zb 194, p. 471; CA li, 1467.)

76. Powell, M.J.D. The local dependence of least squares cubic splines. SI£1 J. Numer. Anal. 6 (1969), 398-413. (MR iL, 1]92; Zb 183,-p. 441; CR l!, 198]2; BS~, 13246.)

77. Ri ce, J. R. The approximation of functions. Vol. II: Nonlinear and multivariate theory, pp. 123-167. Addison-Wesley, Reading, 1969. (MR 39, 5989; Zb 185, p. 306; CR~, 21238; BS 30, 17880.)

- 31 -

78. Rice, J.R. Approximation formulas for physical data. Pyrodynamics 6 (1969), 231-256. (RJM (1970), 12B956.)

79. Rice, J.R. On the degree of convergence of nonlinear spline approximation.

1969

in; Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 349-365. Acad. Press, New York, 1969. (MR~, 2226.)

80. Ritter, K. GE.neralized spline interpolation and nonlinear programming. in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 75-117. Acad. Press, New York, 1969.

8 1. Ri t t e r, K. Two dimensional splines and their extremal properties. Z. Angew. Math. Mech. 49 (1969), 597-608. (MR 40, 6128; Zb 194, p:- 95; RJM (1970), 5B779; BS l!,., 9890.)

82. Rivlin, T.J. An introduction to the approximation of functions, pp. 104-119. Blaisdell Publ. Co., Waltham, 1969. (XR 40, 3126; Zb 189, p. 66.)

83. Sakai, M. Error estimation on piecewise Hermite interpolation. Mem. Fac. Sci. Kyushu Univ. Ser. A 23 (1969), 71-78. (MR 42, 6467; Zb 201, p. 77; BS l!,.,--19638.)

84. Schaback, R. * Spezielle rationale Splinefunktionen (Dissertation).

Universitat Munster, Munster, 1969.

85. Schoenberg, I.J. Monosplines and quadrature formulae. in: Theory and applications of spline functions; ed. by T.N.E. Greville, pp. 157-207. Acad. Press, New York, 1969. (MR~, 3202; Zb 203, p. 370.)

86. Schoenberg, I.J. * Approximations with special emphasis on spline functions (Proc. Symp.

Math. Res. Center, Univ. Wisconsin, May 1969); ed. by I.J. Schoenberg. Acad. Press, New York, 1969. (MR 40, 4638; BS ~, 6605.)

87. Schoenberg, I.J. Cardinal interpolation and spline functions. J. Approximation Theory 2 (1969), 167-206. (HR il, 2266; Zb 202, p. -348.)

88. Schoenberg, I.J. Spline interpolation and the higher derivatives. in: Number theory and analysis (papers in honor of Edmund Landau), pp. 279-295. Plenum, New York, 1969. (MR il, 5848; RJM (1969), 10B105.)

- 32 -

89. Schonefeld, S.A. * A study of products and sums of Schauderbases 1n Banach spaces

(Doctoral dissertation). Purdue Univ., Lafayette, 1969. (DA 30, 5149-B.)

90. Schonefeld, S.A. Schauder bases in spaces of differentiable functions. Bull. Amer. Math. Soc. 21 (1969), 586-590. (HR 12.., 6067.)

91. Schultz, M.H. Error bounds for the Rayleigh-Ritz-Galerkin method. J. Math. Anal. Appl. 27 (1969), 524-533. (MR 40, 373 1; BS ,!.!., 781 7 • )

92. Schultz~ M.H. Multivariate spline functions and elliptic problems.

1969

in: Approximations with special emphasis on spline functions; ed. by I.J. Schoenberg, pp. 279-347. Acad. Press, New York, 1969. (MR~, 2210.)

93. Schultz, M.H. Multivariate L-spline interpolation. J. Approximation Theory 2 (1969), 127-135. (MR 40, 3138; Zb 202, p.-349.)

94. Schultz, M.H. LOO-multivariate approximation theory. SIAM J. Numer. Anal. 6 (1969), 161-183. (MR 40, 4639a; Zb 202~ p. 159; RJM (1970), 5B684; CR!l, 19810; CA lit 76.)

95. Schultz, M.H. L2-multivariate approximation theory. SIAM J. Numer. Anal. 6 (1969), 184-209. (MR 40, 4639b; Zb 202~ p. 159; RJM (1970), 5B685; CA li, 77.)

96. Schultz, M.H. L2-approximation theory of even order multivariate splines. SIAM J. Numer. Anal. 6 (1969),467-475. (Hll. 41, 1193; Zb 198,-p. 400; RJM (1970), 5B778; CR!l, 19642; BS 31, 12880.) -

97. Schultz, M.H. Rayleigh-Ritz-Galerkin methods for multidimensional problems. S:AM J. Numer. Anal. 6 (1969), 523-538. (MR~, 7859; Zb ~,-p. 193; CR!l, 20346; CA li, 1193; BS ,!.!., 20275.)

98. Schultz, M.H. Approximation theory of multivariate spline functions in Sobolev spaces. SIAM J. Numer. Anal. 6 (1969), 570-582. (MR~, 7823; Zb ~,-p. 188; CR~, 21240; CA li, 1179; BS,!.!., 20274.)

99. Schultz, M.H. The Galerkin method for nonselfadjoint differential equations. J. Math. Anal. Appl. 28 (1969), 647-651. (ZB 197, p. 137; BS 31, 15921.)

- 33 - 1969

100. Schumaker, L.L. Approximation by splines. in: Theory and applications of spline functions; ed. by T.N.E. Greville, pp. 65-85. Acad. Press, New York, 1969. (MR~, 686; Zb 187~ p. 328.)

101. Sch~kert L.L. Some algorithms for the computation of interpolating and approximating spline functions. in: Theory and applications of spline functions; ed. by.T.N.E. Greville, pp. 87-102. Acad. Press~ New York, 1969. (MR 39, 687; Zb 188, p. 223.)

102. Schumaker, L.L. On the smoothness of best spline approximations. J. Approximation Theory 2 (1969), 410-418. (MR~, 4076; Zb 183, p.-59; BS ~t 9399.)

103. Sharma, A.; Meir, A. Convergence of a class of interpolatory splines. in~ Abstract spaces and approximation (Proc. Conf. Oberwolfach, 1968); ed. by P.L. Butzer and B.S. Nagy, pp. 373-374. Birkhauser Verlag, Basel, 1969. (Zb 187, p. 329; BS ~, 9426.)

104. Simpson, R.B. The Rayleigh-Ritz process for the simplest problem in the calculus of variations. SIAM J. Numer. Anal. ~ (1969), 258-271. (MR 40, 5 122. )

105. Sims, S.E. * Convergence properties of spline functions (Doctoral dissertation).

Univ. of Arizona, Tucson, 1969. (DA30,3763-B.)

106. Sonnevsld, P. Errors in cubic spline interpolation. J, Engrg. Math. 3 (1969), 107-117. (MR 40, 601; Zb 183, p. 442; RJM (1969), 12B874; BS ~, 3]31.)

107. Spath, H. Algorithmus 10: Zweidimensionale glatte Interpolation; Twodimensional smooth interpolation. Computing 4 (1969), 178-182. (RJM (1969), 12V569; CA Q, 2431; BS 11,3141.)

108. Spath, H. Exponential spline interpolation. Computing 4 (1969), 225-233. (MR 40, 2216; Zb 184, p. 198; RJM (1970), 3B877; CR~, 18512; CA 13, 3156; BS 31, 8074.)

109. Spath, H. Algorithm 40: Spline interpolation of degree three. Comput. J. 12 (1969), 198-199. (CA Q~ 3144b.)

- 34 -

110. Spath, :1. Algorithm 42: Interpolation by certain quintic splines. Comput. J. 12 (1969), 292-293. (CA li, 356b.)

Ill. Spath, H.

1969

* Die numerische Berechnung von interpolierenden Spline-Funktionen mit Blockunterrelaxation (Dissertation). Universitat Karlsruhe, Karlsruhe, 1969. (MR 42, 8659.)

112. Stephens, A.B. * Convergence of the residual for Ritz-Galerkin approximation (Doctoral

dissertation). Univ. of Maryland, College Park, 1969. (DA ll, 296-B.)

113. Storchai, V.F. The deviation of polygonal functions in the Lp metric. Mat. Zametki 5 (1969), 31-37 (Russian). Translated as-Math. Notes 5 (1969), 21-25. (MR 39, 688; Zb ~, p. 88; RJM (1969), 8B84; BS 30, 12374.)

114. Studden, W.J.; Van Arman, D.J. Admissible designs for polynomial spline regression. Ann. Math. Statist. 40 (1969), 1557-1569. (MR 40, 2195.)

115. Subbotin, Yu.N. Piecewise-polynomial interpolation (Russian). in: Poisk Ekstremuma., Tomskir Inst., Tomsk (1969), 248. (RJM (1970), 5B137.)

116. Swartz, B.; Wendroff, B. Generalized finite-difference schemes. Math. Compo 23 (1969), 37-49. (MR~, 1125;-Zb 184, p. 385; RJM (1970), IB771; BS 30, 14601.)

117. Tihomirov, V.M. Best methods of approximation and interpolation of differentiable func­tions in the space C[-I,I]. Mat. Sb. 80 (1969), no. 122, 290-304 (Russian). Translate~as Math. USSR-Sb. 9 (1969), 275-289. (MR i!., 703; Zb 204, p. 133; BS ll, 9390.)

118. Varga, R.S. Error bounds for spline interpolation. in: Approximations with special emphasis on spline functions; ed. by 1.J. Schoenberg, pp. 367-388. Acad. Press, New York, 1969. (MR 40, 6 130. )

119. Wakoff, G.1. * Piecewise polynomial spaces and their use with the Rayleigh-Ritz­

Galerkin method (Doctoral dissertation). Harvard Univ., Cambridge (Mass.), 1969.

- 35 -

120. Wendroff, B. First principles of numerical analysis, pp. 62-67. Addison-Wesley, Reading, 1969. (Zb 194, p. 178; BS 30, 1$456.)

121. Woodford, C.H. Smooth curve interpolation. BI! 9 (1969), 69-77. (R.JM-(1969), IIB715; CR lQ., 18077; BS~, 1624.)

122. Young, J.D. Ge11eralization of segmented spline fitting of third order. The Logistics Review 5 (1969), no. 23, 33-40. (R~~ (1970), 4B947; CR~, 19819.)

123. Zavjat'ov, Yu. S. Interpolation with piecewise polynomial functions in one and two variables (Russian). Mat. Probl. Geofiz. (Novosibirsk) l (1969), 125-141. (RJN (1970), IIB861.)

124. Ziegler, Z. One-sided L1-approximation by splines of an arbitrary degree.

1970

in~ Approximations with special emphasis on spline functions; ed. by I..T. Schoenberg, pp. 405-413. Acad. Press, New York, 1969. (MR 40, 7684.)

1970

1. Ahlberg, J .H. Spline approximation and computer-aided design. in: Advances in Computers, Vol. 10; ed. by F.L. Alt and M. Rubinoff, pp. 275-289. A~ad. Press, New York, 1970. (RJM (1971), IOB824; CR~, 21239; BS ~, 5046.)

2. Ahlberg~ J.H.; Nilson, E.N. Polynomial splines on the real line. J. Approximation Theory 3 (1970), 398-409. (Zb 215, p. 177; RJM (1971), IOB55; CR.!.i, 23024.)

3. Akima, H. A new method of interpolation and smooth curve fitting based on local procedures. J. Assoc. Comput. Mach. 17 (1970), 589-602. (Zb 209, p. 468; RJM (197l), 6B930; CA~, 99; BS 32, 1208.)

4. Atteia, M. Fonctions "Spline" et noyaux reproduisants d'Aronszajn-Bergman. R2V. Fran~aise Informat. Recherche Operationnelle ~ (1970), no. R-3, 31-43. (RJM (1971), 12B806; BS ~, 4653.)

5. Barrar, R.B.; Loeb, H.L. Existence of best spline approximations with free knots. J. Math. Anal. Appl. 31 (1970), 383-390. (MR~, 8887; Zb 194,-p. 368; RJM (1971), 5B119; BS~, 19622.)

- 36 - 1970

6. Berkovitz, L.D.; Pollard, H. A n~n-classical variational problem arising from an optimal filter problem. II. Arch. Rational Mech. Anal. 38 (1970), 161-172. (14R 42, 5138; RJM (197]), 6B530.)

7. Birkhoff, G.; Fix, G. Accurate eigenvalue computations for elliptic problems. in~ Numerical solution of field problems in continuum physics (SIAM-AMS Proc., vol. 2); ed. by G. Birkhoff and R.S. Varga, pp. 111-151. Amer. Math. Soc., Providence (R.I.), 1970. (MR~, 4827; Zb 231, 65087.)

8. Bosarge Jr., W.E.; Johnson, O.G. Dirp.ct method approximation to the state regulator control problem using a Ritz-Trefftz suboptimal control. IEEE Trans. Automatic Control AC-15 (1970), 627-631. (cf. MR 42, 7334; RJM (1971), 4B609; BS ~, 8883.)

9. Bramble, J.H.; Hilbert, S.R. EBtimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIN1 J. Numer. Anal. 7 (1970), 112-124. (MR~, 7819; Zb 201,-p. 78; RJM (1971), IB835; CR ll, 19963; CA li, 2086.)

10. Bramble, J.H.; Schatz, A.H. Rayleigh-Ritz-Galerkin methods for Dirichlet's problem using subspaces without boundary conditions. Cm!lIll.. Pure Appl. Math. 23 (1970), 653-675. (MR 42, 2690; Zb 195, p--. 388; RJM (1971), 6B880.)

1 1. Case, J. R. * Extensions and generalizations of Jackson's theorem (Doctoral disserta­

tion) • Syracuse Univ., Syracuse, 1970. (DA 32, 1066-B.)

12. Cavaretta Jr., A.S. * On cardinal perfect splines of least sup norm on the real axis

(Doctoral dissertation). Univ. of Wisconsin, Madison, 1970. (DA 1l, 6740-B.)

13. Chan, P.P.-Y. * Approximation theory with emphasis on spline functions and applications

to differential and integral equations (Doctoral dissertation). Case Western Reserve Univ., Cleveland, 1970. (DA 1l, 4191-B.)

14. Cheney, E.W.; Schurer, F. Convergence of cubic spline interpolants. J. Approximation Theory 3 (1970), 114-116. (MR 40, 7680; Zb 193, p.-25; RJM (1970). IOB795; BS 1l, 12879.)

15. Cheney, E.W.; Price, K.H. Minimal projections. in: Approximation theory (Proc. Symp., Lancaster, July 1969); ed. by A. Talbot, pp. 261-289. Acad. Press, London, 1970. (MR~, 751; Zb 217, p. 162; CR..!l, 20847.)

- 37 - 1970

16. Chi~ D.N.-H. * Linear multistep methods based on g-splines (Doctoral dissertation).

Univ. of Pittsburgh, Pittsburgh, 1970. (DA 1l, 2812-B.)

17. Chu, S.C. Piecewise polynomials and the partition method for nonlinear ordinary differential equations. J. Engrg. Math. 4 (1970), 65-76. (MR i!~ 2933; Zb-208, p. 418; BS 1l, 17671.)

18. Ciarlet, P.G.; Varga, R.S. Discrete variational Green's function. II: One dimensional problem. Numer. Math. 16 (1970), 115-)28. (MR~, 1440;RJM (1971), 6B284; CR g, 21752; CA.!2., 825; BS 32, 1231.)

19. Ciarlet, P.G.; Natterer, F.; Varga, R.S. Numerical methods of high-order accuracy for singular nonlinear boundary • value problems. Numer. Math. 15 (1970), 87-99. (MR 43, 1439;RJM (1971), 3B598; CR g, 20698; BS 32, 1895.)

20. Covaci-Munteanu, M.J. * C~ntributions a la theorie des fonctions splines a une et a plusieurs

variables (These). Universite Catholique de Louvain, Louvain, 1970.

21. Curtis, A. R. The approximation of a function of one variable by cubic splines. iu: Numerical approximation to functions and data; ed. by J.G. Hayes, Pi? 28-42. Athlone Press, London, 1970. (CR.!.!., 20155.)

22. Delvos, F.J.; Schempp, W. On spline systems. Monatsh. Math. 74 (J970), 399-409. (MR~, 2399; Z~203, p. 122; RJM (1971), 7B890.)

23. Dobysh, A.D. Construction of interpolating piecewise polynomial functions (Russian).

v v ~ Trudy 3-~ Zymn. Skoly po Mat. Programmir. i Smezi. Vopr. 2 (1970), 279-299. (RJM (1971), 7B999.)

24. Dobysh, A.D. A constructive representation of smooth curves and surfaces (Russian). Sb. Trudy Mosk. In~.-Stroit. Inst. (1970), no. 83, 107-123. (RJM (1971), 9B53.)

25. Douglas Jr., J.; Dupont, T. Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 7 (1970), 575-626. (MR 43, 2863; RJM (1971), 7B953; CR g, 21750; CA.!2., 1]02; BS ~, 3495.)

26. Ducatea~, Ch.F. Acceleration de convergence pour une extrapolation utilisant les fonctions splines. in: Procedures Algol en Analyse Numerique II, pp. 79-82. Centre National de 1a Recherche Scientifique, Paris, 1970.

- 38 - 1970

27. Fitzgerald, J.M. * Numerical methods using integrals over suhregions (Doctoral dissertation).

The Pennsylvania State Univ., University Park, 1970. (DA 32, 1070-B.)

28. Freud, G.; Popov, V.A. Some questions that are related to the approximation by spline functions e.nd polynomials (Russian). Studia Sci. Math. Hungar. 5 (1970), 161-171. (MR 42, 2225; Zb 201, p. 396.)

29. Fyfe, D.!. Th~ use of cubic splines in the solution of certain fourth order boundary value problems. Comput. J. 13 (1970), 204-205. (i'iR 41, 6407; Zb 191, p. 167; RJM (1970), IIB865; CA..!!!.., 2110; BS 31, 20394.) -

30. Gaier, D. Saturation bei Spline-Approximation und Quadratur. Numer. Math. 16 (1970), 129-140. (MR 42, 8692;:Zb 188, p. 223; RJM (1971), 5B1108; CR~, 21565; CA 15, 838; BS 32~202.)

3 1. Galkin, P. V • Th~ possibility of periodic spline interpolation. Mat. Zametki 8 (1970), 563-574 (Russian). T~anslated as-Math. Notes 8 (1970), 786-791. (lb 221,41011; RJM (1971): 3B95; BS ~, 2603.)

32. Gerald, C.F. Applied numerical analysis, pp.290-294. Addison-Wesley, Reading, 1970. (CR~, 20668.)

33. Gold, S. C. * Data smoothing using least-square spline functions (Doctoral disserta­

tion) • Univ. of Utah, Salt Lake City, 1970. (GA~, 4684-B.)

34. Greville, T.N.E. Table for third-degree spline interpolation with equally spaced argu­ments. Math. Compo 24 (1970), 179-183. (MR~, 2885;-Zb 194, p. 471; RJM (1970), 12B953; BS ~, 20290.)

35. Guglielmo, F. di Methode des elements finis: une famille d'approximations des espaces de Sobolev par les translates de p fonctions. Calcolo 7 (1970), 185-233. (Zb 216,-p. 158; BS 32, 6627.)

36. Haimovici, A. Sur une certaine approximation des distributions generalisant des formu.,­lesd'integration, de derivation numerique et d'interpolation. Rev. Roumaine Math. Pures Appl. ~ (1970), 1415-1419.

- 39 -

37. Hammerlin, G. Numerische Mathematik. I, pp. 84-94. ~.I. Hochschulskripten, 498-498a). Bibliographisches Institut, Mannheim, 1970. (MR~, 6381; Zb 1l1, p. 167.)

38. Hands comb , D.C. Characterization of best spline approximations with free knots.

1970

in: Approximation theory (Proc. Symp., Lancaster, July 1969); ed. by A. Talbot, pp. 63-70. Acad. Press, London, 1970. (MR 42, 735; Zb 213, p. 87.)

39. Haussman, W. * Zur Theorie der Spline-Systeme (Habilitationsschrift).

Ruhr-Universitat, Bochum, 1970.

40. Hayes, J.G. Numerical approximation to functions and data (Proc. ConL Inst. Hath. Appl., Canterbury, 1967); ed. by J.G. Hayes. Athlone Press, London (Agents: Tiptree Book Service Ltd, Tiptress, Essex), 1970. (Zb 212, p. \73; CR.!..!., 19948.)

41. Hertling, J. Approximation of piecewise continuous functions by a modification of piecewise Hermite interpolation. Numer. Math. 15 (1970), 404-414. (~IR~, 2223; 194, p. 185; RJM (1971), 3B96; CR~, 21737; CA lit 3268.)

42. Hoskins, W.D. Algorithm 62: Interpolating quintic splines on equidistant knots. Comput. J. 13 (1970), 437-438. (CA.!2., 331}":"")

43. Hung, H. - S • * The numerical solution of differential and integral equations by spline

functions (Doctoral dissertation). Univ. of Wisconsin, Madison, 1970.

44. Ionescu a D.V. Introduction iii la theorie des "fonctions spline". Acta Math. Acad. Sci. Hungar. 21 (1970), 21-26. (MR~, 6470; Zb 206, p. 348; RJM (1970), I1B97; BS 11, 20405.)

45. Ionescu, D.V. La difference divisee d'une fonction de trois variables et sa represen­tation par une integrale triple. Rev. Roumaine Math. Pures Appl. 15 (1970), 1425-1436. (r.fR 43, 6376; Zb 223, 41020.)

46. Janenko, N.N.; Kvasov, B.I. An iterative method for the construction of polycubic spline functions. Dokl. Akad. Nauk SSSR 195 (1970), 1055-1057 (Russian). Translated as Soviet Math. Dokl. 11 (1970), 1643-1645. (HR 43, 2822; Zb 223, 41010; RJM (1971), 4B992; BS ~, 3471.)

- 40 - 1970

47. Janenko, N.N.; Kvasov, B.l. An iterative method for the construction of polycubic spline functions (Russian). Crs],. Metody Meh. Splo~i. Sredy. Inform. Bjul. (1970), no. 3, 84-89. (R;M (1971), 4B907.)

48. Jerome) J.W. Linear self-adjoint mUltipoint boundary valuepr6blems and related approximation schemes. Nl',mer. Math. 15 (1970), 433-449. (Zb 214, p. 418; RJM (1971), 4B916; CA~, 3296; BS 32, 1886.)

49. Kalik, L. Une propriete de minimum des fonctions "spline". Studia Univ. Babef-Bolyai Sere Math.-Mech. ~ (1970), no. 1, 35-46. (MR~. 8889; BS ~, 20299.)

50. Karlin, S.; Karon, J. A remark on B-splines. J. Approximation Theory 3 (1970), 455. (Zb 218, 41002; RJM (1971), 7BI003o)

51. Karliu, S.; Lee, J. Periodic boundary-value problems with cyclic totally positive Green's functions with applications to periodic spline theory. J. Differential Equations 8 (1970), 374-396. (MR 42,3341; Zb 203, p. 1'03; RJM (1971), 6B283.)

52. Kautsky, J. Optimal quadrature formulae and minimal monosplines in Lq • J. Austral. Math. Soc. II (1970),48-56. (MR~, 2277; Zb 187, p-.-20; BS ~, 20297.)

53. Kimeldorf, G.S.; Wahba, Go A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Ann. Math. Statist. 41 (1970), 495-502. (MR 40, 8206; Zb I 93:-p. 452.)

54. Kimeldorf, G.S.; Wahba, G. Spline functions and stochastic processes. Sankhya Sere A 32 (1970), 173-180.

55. LaFata, P.; Rosen, JoB. An interactive display for approximation by linear programming. Camm. ACM 13 (1970), 651-659. (MR 42, 2712; Zb 217, p. 225; CR~, 21067; CA~, 96.)

56. Langhaa~, H.L.; Chu, s.c. Piecewise polynomials and the partition method for ordinary differential eqt:.ations. in: Developments in theoretical and applied mechanics, Vol. 4 (Proc. Fourth Southeastern Conf., New Orleans (La.), 1968); ed. by D. Frederick, pp. 553-564. Pergamon Press, Oxford, 1970. (MR~. 9447.)

- 41 - 1970

57. Langner, W. Die Losung des Strakproblems bei empirischen Funktionen mittels stuck­weieer kubischer Polynome. Elektron. Rechenanl. 12 (1970), 262-269. (RJM (1971), 3B600; BS-32 , 3476.)

58. Levina, M. On the convergence of the approximate solutions of a boundary value problem by spline functions (Russian; English summary). Trudy Tallin. Politehn. lnst. Ser. A 293 (1970), 3-9. (R..TM (1970), 10B713.) -

59. Levina, M. On the mean-root-square error for some spline functions (Russian; English summary). Trudy Tallin. Politehn. Inst. Ser. A 293 (1970), 11-]4. (MR 43, 7820; RJM (1970), 10B796.)

60. Lipow, P.R. * Cardinal Hermite spline interpolation (Doctoral dissertation).

Univ. of Wisconsin, Madison, 1970. (DA 1!, 6128-B.)

61. Loginov, A.S. Estimates for the approximation by polygonal lines of continuous func­tions of class Hw (Russian). Vestnik Mosk. Univ. Ser. I Mat. Meh. 25 (1970), no. 6, 47-55. (MR 44, 3058; Zb 215, p. 462; RJM (197]), 4BI08.)

62. Lucas, !.R. * A theory of generalized splines with applications to nonlinear boundary

value problems (Doctoral dissertation). Georgia Institute of Technology, Atlanta, 1970. (DA 1!, 355S-B.)

63. Lucas, T.R. A generalization of L-splines. Numer. Math. 15 (1970), 359-370. {MR 42, 3976;-zh 214, p. 4]3; RJM (]97]), SB126; CA li, 3295; BS~, 1845.)

64. Marsaglia, G. One-sided approximations by linear combinations of functions. in: Approximation Theory (Proc. Symp., Lancaster, July 1969); ed. by A. Talbot, pp. 233-242. Acad. Press, London, 1970. (l{R 42, 1307; CR~, 21050.)

65. Marsden, M.J. An identity for spline functions with applications to variation­diminishing spline approximation. J. Approximation Theory 3 (1970), 7-49. (MR 40, 7682; Zb 192, p.-421; BS 1!, 12874.)

66. McClure, D.E. * Feature selection for the analysis of line patterns (Doctoral disserta­

tion). Brown Univ., Providence, 1970. (DA 1!, 7439-B.)

- 42 - 1970

·67. McConalogue, D.J. A quasi-intrinsic scheme for passing a smooth curve through a discrete set of points. Cvmp. J. 13 (I 970), 392-396. (CR 12, 21066.)

68. Meinguet, J. Optimal approximation and interpolation in normed spaces. in~ Numerical approximation to functions and data; ed. by J.G. Hayes, pp. 143- I 57. Athlone Press, London, 1970. (CR 12, 20850.)

69. Mishra, B.N.; Mahto, K.R. Interpolation by generalized Tchebycheffian spline functions. Ranchi Univ. Math. J. I (1970), 1-10. (~lR 43, 3698.)

70. Moler, C.B.; Solomon, L.P. U£e of splines and numerical integration in geometrical acoustics. J. Acoustical Soc. Amer. 48 (1970), 739-744.

71. Morozov, V.A. On the problem of differentiation and some algorithms for the approxima­tion of measured data (Russian). Sb. Rabot Vycisl. Centra Mosk. Univ. ~ (1970), 46-62. (RJM (1971), IB732.)

72. Natterer, F. Schranken fur die Eigenwerte gewohnlicher Differentialgleichungen durch Spline-Approximation. Numer. Math. 14 (1970), 346-354. (MR~, 6413;:Zb ~, p. 184; CR~, 19991; CA~, 2105; BSll, 15932.)

73. Nielson, G.M. * Surface approximation and data smoothing using generalized spline func­

tions (Doctoral dissertation). Ulliv. of Utah, Salt Lake City, 1970. (DA ll, 2833-B.)

74. Nilsor., E.N. Cubic splines on uniform meshes. Comm. ACM 13 (1970), 255-258. (MR 44, 1189; Zb 214, p. 414; RJM (1971), 4BI002; CR 12, 21733; BS 31, 17930.) -

75. Nitsche, J. Lineare Spline-Funktionen und die Methoden von Ritz fur elliptische Randwertprobleme. Arch. Rational Mech. Anal. 36 (1970), 348-355. (fIR 40, 8250; Zb 192, p. 445; BS ll, 15926.)

76. Nitsche, J. Zur Konvergenz von Naherungsverfahren bezuglich verschiedener Normen. Numer. Math. 15 (1970), 224-228. (MR 43, 5231;:Zb 221, 65092; CR ll, 22814; BS~, 1201.)

- 43 - 1970

77. Parker, J.B. Methods of graduating heterogeneous data. in: Numerical approximation to functions and data; ed. by J.G. Hayes, pp • 1 1 1- I 14. Athlone Press, London, 1970. (CR~, 20514.)

78. Parker, K. Experience with cubic splines in the graduation of neutron cross-section data. in: Numerical approximation to functions and data; ed. by J.G. Hayes, pp. 107-110. Athlone Press, London, 1970. (Ck~, 19959.)

79. Pereyra, V. Highly accurate numerical solution of casilinear elliptic boundary­value problems in n dimensions. Math. Compo 24 (1970), 771-783. (Zb 219, 65084; CA.!i, 1681; BS E. 5728.)

80. Popov, V.A.; Sendov, B.H. Classes characterized by best-possible approximation by spline functions. Mat. Zametki 8 (1970), 137-148. (Russian). Translated as-Math. Notes 8 (J970), 550-557. (MR 43, 5224; Zb 201, p. 395.)

81. Powell, M.J.D. Curve fitting by splines in one variable. in: Numerical approxi~ation to functions and data; ed. by J.G. Hayes, pp. 65-83. Athlone Press, London, 1970. «(;R~, 20157.)

82. Price, H. S.; Varga, R. S. Error bounds for semidiscrete Galerkin approximations of parabolic problems with applications to petroleum reservoir mechanics. in: Numerical solution of field problems in continuum physics (SIAM-AMS Proe., vol. 2); ed. by G. Birkhoff and R.S. Varga, pp. 74-94. Amer. Math. Soc., Providence (R.I.), 1970. (MR 42, 1358.)

83. Priver, A.S. * Data smoothing in interactive computer graphics (Doctoral dissertation).

Harvard Univ., Cambridge (Mass.), 1970.

84. Rice, J.R. General purpose curve fitting. in: Approximation theory (Proc. Symp., Lancaster, July 1969); ed. by A. Talbot, pp. 191-204. Acad. Press, London, 1970. (MR 42, 2632; Zb 215, p. 552; CR~, 21047.)

85. Richards, F.B. * A generalized minimum norm property for spline functions with applica­

tions (Doctoral dissertation). Univ. of Wisconsin, Madison, 1970. (DA l!., 6 763-B.)

- 44 - 1970

86. Ritter, K. Twe-dimensional spline functions and best approximations of linear functionals. J. Approximation Theory 3 (1970), 352-368. (MR~, 8138; Zb 203, p.-370; RJM (1971), 10B60; CR~, 22327.)

87. Rosman, B.H. ~ Extension of results by Rice and Schumaker on spline approximation. SIAM J. Numer. Anal. 7 (1970), 314-316. (MR~, 2633; Zb 208,-p. 406; RJM (1971), 4Bl11; CR l!, 20348; BS 32, 493.)

88, Russell, R.D. * I. Existence of eigenvalues for integral equations;

II. A collocation method for boundary value problems (Doctoral disserta­tien). New Mexico State Univ., Las Cruces, 1970. (DA 2!, 7446-B.)

89. Sakai, H. Spline interpolation and two-point boundary value problems. Me~. Fac. Sci. Kyushu Univ. Ser. A 24 (1970), 17-34. (MR 42, 8702; Zb 201, p. 78; BS 32,--1190.)

90. Sakai, H .• Multi-dimensional cardinal spline function and its applications. Me~. Fac. Sci. Kyushu Univ. Ser. A 24 (J970), 40-46. (MR43, 4268; Zb 201, p. 78; RJM (1971), IB948; BSE., 1189.)

91. Sale, A.H.J. Note on algorithm 42: Interpolation by certain quintic splines. Comput. J. 11 (1970), 115.

92. Schechter, E. Error bounds in the numerical integration of differential equations. Studia Univ. Babef-Bolyai Ser. Math.-Mech. ~ (1970), no. 1, 47-53. (MR~, 1343; RJM (1970), IIB810;)

93. Schempp, W. On spaces of distributions related to Schoenberg's approximation theorem. Math. Z. 114 (1970), 340-348. (MR 42, 2235; Zb 182, p. 457.)

94. SchemJ,?p, W. * Uber Spline-Grundraume (Habilitationsschrift).

Ruhr-Universitat, Bochum, 1970.

95. Scherer, K. On the best approximation of continuous functions by splines. SIAM J. Numer. Anal. 7 (1970), 418-423. (MR 42, 2634; Zb 206,-p. 348; RJM (1971), 5B118; CR~, 20854; CA 14, 3287; BS 32, 1851.)

96. Schoenberg, I.J. A second look at approximate quadrature formulae and spline interpolation. Advances in Math. 4 (1970), 277-300. (M.,{ i!., 8895; Zb 215, p. 175; RJM (197J), IB937; BS E, 1211.)

- 45 -

• 97. Schoenb~rg, I.J.; Ziegler, Z.

On cardinal monosplines of least Loo-norm on the real axis. J. Analyse Math. 23 (1970), 409-436. (i1R~, 782; Zb 217, p. 138; RJM (1971), IB92.)

98. Schoenoerg, I.J. Cardinal interpolation and spline functions.

1970

in: Inequalities II (Proc. 2nd Symp. Inequalities U.S. Air Force Acad., Colorado, 1967); ed. by O. Shisha, pp. 335-374. A~ad. Press, New York, 1970.

99. Schultz, M.H. Elliptic spline functions and the Rayleigh-Ritz-Galerkin method. Math. Compo 24 (1970), 65-80. (11R 1l, 9448;-RJM (1971), 5BI036; BS ~, 20282.)

100. Schultz, M.H. Error bounds for polynomial spline interpolation. Math. Compo 24 (1970), 507-515. (MR 43, 783;:Zb 216, p. 230; RJM (1971), IIBII05; CA~, 1420; BS 32, 5693.)

101. Schultz, M.H. The condition number of a class of Rayleigh-Ritz-Galerkin matrices. Bull. Amer. Math. Soc. 76 (1970), 840-844. (MR~, 4276; Zb 225, 65054.)

102. Schurer, F. A note on interpolating periodic quintic spline functions. in: Approximation theory (Proc. Symp., Lancaster, July 1969); ed. by A. Talbot, pp. 71-81. Acad. Press, London, 1970. (I1R 42, 757; Zb 214, p. 3 16 . )

103. Sendov, B.; Popov, V.A. The approximation by spline-functions (Russian). C.R. Acad. Bulgare Sci. 23 (1970), 755-758. (MR 43, 7828; Zb 209, p.-g6.)

104. Shah, J. t-l. Two~dimensional polynomial splines. Numer. Math. 15 (1970), 1-14. (MR 42, 5421;:Zb 181, p. 176; RJM (1970), IOB791; CR.!.!., 20345; CA 14, 2415; BS 31, 17641.)

105. Shu, H.; Hori, S.; Mann, W.R.; Little, R.N. The synthesis of sculptured surfaces. in: Numerical control programming languages (Proc. First Intern. IFIP/IFAC PROLAMAT Conf., Rome, 1969), pp. 358-375. North-Holland Publ. Co., Amsterdam, 1970. (CR j2, 21055.)

106. Subbotin, Yu.N. Approximation of functions of class wkH~ by m-order splines. Dokl. Akad. Nauk SSSR 195 (1970), 1039-1041 (Russian). Translated as Soviet Math. Dokl. II (1970), 1626-1628. (MR 42, 8139; Zb 227, 41004; BS 32, 3470.)

- 46 - 1970

107. Subbotin, Yu.N.; Chernykh, N.I. Th£ order of the best spline approximations of certain classes of func­tions. Mat. Zametki 7 (1970), 31-42 (Russian). Translated as-Math. Notes 7 (1970), 20-26. (MR~, 4077; Zb 195, p. 351; RJM (1970), 5B131; BS ll, 12886.)

108. Subbotin. Yu.N. Diruaeter of class WrL in L(0,2w) and spline function approximation. ~~t. Zametki 7 (1970), 43-52 (Russian). Translated as-Math. Notes 7 (1970), 27-32. (MR~, 4078; Zb 195, p. 71; BS ll, 13091.)

109. Subbotin r Yu.N. On a linear method for the approximation of differentiable functions. Mat. Zametki 7 (1970), 423-430 (Russian). Translated as-Math. Notes 7 (1970), 256-260. (MR 42, 4930; Zb 194, p. 367; BS ll, 17397.)

110. Subbotin, Yu.N. The basis in C(O,2w) (Russian). in~ Trudy Centro Zonal'n Ob'edin. Mat. Kafedr. Kalinin. Gos. Ped. Inst. 1 (1970), 141-144. 1MR~, 6472; RJM (1971), 8B511.)

III. Swartz, B.~.

* O(hk-J w(Dkf,h» bounds on some spline interpolation errors (Doctoral dissertation). New York Univ., New York City, 1970. (RJM (1972), 2B880; DA~, 441-B.)

112. Terekhov, T.S. On a linear positive piecewise polynomial operator (Russian). U(en. Zap. Stavropol. Gos. Ped. Inst. Mat., Stavropol' (1970), 63-65. (~TM (1971), 2B98.)

113. Thomann, J. * Determination et construction de fonctions spline a deux variables

definis sur un domaine rectangulaire ou circulaire (These). Universite de Lille, Lille, 1970.

114. Thomanr., J. Obtention de 1a fonction spline d'interpo1ation a 2 variables sur un domaine rectangu1aire ou circulaire. in: Procedures Algol en Analyse Numerique II, pp. 83-94. Centre National de la Recherche Scientifique, Paris, 1970.

115. Tihomirov, V.M. * Some problems in approximation theory (Russian) (Doctoral dissertation).

Moscow State University, Moscow, 1970.

116. Varga, R.S. Accurate numerical methods for nonlinear boundary value problems. in: Numerical solution of field problems in continuum physics (SIAM-AMS Proc., vol. 2); ed. by G. Birkhoff and R.S. Varga, pp. 152-167. Amer. Math. Soc., Providence (R.I.), 1970. (MR 42, 2650; Zb 221, 65130.)

- 47 - J970

117. Varga, R.S. Accurate numerical methods for nonlinear boundary value problems. in! Numerical solutions of nonlinear problems (Studies in Numerical Analysis, no. 2); ed. by J.M. Ortega and W.C. Rheinboldt, pp. 99-113. Sec. Indust. Appl. Math., Philadelphia (Pa.), 1970. (MR 42, 4026; Zb 226, 6S0S9.)

1]8. Vedeneev, E.P.; Zhidkov, N.P.; Shchedvin, B.M. Differentiation of a tabular function by the method of interpolating cor.jugation. Z. Vy~isl. Mat. i Mat. Fiz. 10 (1970), 433-437 (Russian). Trauslated as USSR Comput. Hath. and Math. Phys • .!.Q. (1970), no. 2, 200-207. (MR 44, 1221; RJM (1970), 8B816.)

119. Velikin, V.L. Best approximations of continuous functions by spline functions. Mat. Zametki 8 (1970), 41-46 (Russian). Translated as-Math. Notes 8 (1970), 492-495. (MR 42, 3474; Zb 20S, p. 368.)

120. Velikin, V.L.; Zhensykbaev, A.A. Some properties of fundamental spline functions (Russian). in! Sb. Rabot Aspirantov Dnepropetr. Univ. Meh. Mat., Dnepropetrovsk (1970), 42-47. (RJM (1970), IIBI15.)

121. Woodford, C.H. An algorithm for data smoothing using spline functions. BIT 10 (1970), 501-S10. (Zb 214, p. 414; RJM (1971), 9B74S; CR ll, 23817; CA~, 849; BS ~, 3768.)

122. Young, J.D. Function and first derivative fitting by modified quintic spline. The Logistics Review 6 (1970), no. 27, 33-39. (RJM (1971), SBI141.)-

123. Young, J.D. An optimal cubic spline. The Logistics Review 6 (1970), no. 29, 33-37. (RJM (1971), l1BI102.)

124. 'Yuille, I.M. A system for on-line computer aided design of ships-prototype system and future possibilities. Trans. Roy. Inst. Naval Architects ~ (1970), 443-463.

12S. Zafarullah, A. A method of numerical solution of functional equations. J. Optim~zation Theory Appl. 5 (1970), 283-288. {MR~, 2702; Zb~, p. 191;-RJM (1971), 8B706.)

126. Zavjalov, Yu.S. On the use of numerical methods for the solution of complex construction pro~lems in mechanical engineering (Russian). Vy~isl. Sistemy 38 (1970), 3-22.

127. Zavjalov, Yu.S. Interpolation with cubic splines (Russian). Vy~isl. Sistemy 38 (1970), 23-73. (RJM (1971), IB95l; BS 32,1185.)·

- 48 - 1971

128. Zavjalov, Yu.S. Interpolation with bicubic splines (Russian), Vy~isl. Sistemy 38 (1970), 74-101. (RJM (1970), 12B955; BS~, 1831.)

129. Zavjalov, Yu.S. An optimal property of cubic spline functions and the problem of smoothing (Russian). Vytisl. Sistemy 42 (1970), 89-108. (RJM (1971), 7B989; BS 33, 23.)

130. Zavjal~v, Yu.S. An optimal property of bicubic spline functions and the problem of smoothing (Russian). Vy~isl. Sistemy 42 (1970), 109-158. (RJM (1971), 7B995; BS 1l, 23.)

1971

1. Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L. Complex polynomial splines on the unit circle. J. ~ath. Anal. Appl. 33 (1971), 234-257. (MR~, 3696; RJM (1972), 4B174; BS 32, 3472.)

2. Albasiny, E.L.; Hoskins, w.n. The numerical calculation of odd-degree polynomial splines with equi­spaced knots. J. Inst. Math. Appl. 7 (1971), 384-397. (Zb 217, p. 423; RJM (1972), 3B814; BS 32, 7169.)

3. Anderssen, A.S.; White, E.T. Improved numerical methods for Volterra integral equations of the first kind. Comput. J. 14 (1971), 442-443. (Zb 227, 65064; CA~, 346; BS 33, 7072.)

4. Atteia, M. Fonctions "spline" dans Ie champ complexe. C.R. Acad. Sci. Paris Ser. A 273 (1971), 678-681. (RJM (1972), 3B819; BS 1l, 1048-.)

5. Aubin, J.P. Remarks about the construction of optimal subspaces of approximants of a Hilbert space. J. Approximation Theory 4 (1971), 21-36. (Zb 224, 46021.) -

6. Aubin, J.P.; Burchard, H.G. Some aspects of the method of the hypercircle applied to elliptic variational problems. in: Numerical solution of partial differential equations II; ed. by B.E. Hubbard, pp. 1-67. Acad.Press, New York, 1971. (l'I'~ 44, 2359.)

7. Bacopoulos, A.; Marsden, M. On a map from the splines into a positive cone with applications. Aequationes Math. 7 (1971), 122-124. (RJM (1972), 8B797~)

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8. Baviock, H.; Gautschi, W.; Willems, G.M. Colloquium Approximatietheorie, pp. 10-]5 (MC syllabus, no. 14). Mathematisch Centrum, Amsterdam, 1971.

9. Bellman, R.; Roth, R.S.

1971

The use of splines with unknown end points in the identification of systems. J. Math. Anal. Appl. 34 (1971), 26-33. (MR 43, 3005; Zb 217,-p. 116; RJM (1972), 4Bl111; CR ll, 23214.)

10. Belov, Yu.A. On the algorithm of piecewise polynomial approximation (Russian). Vy~isl. Prikl. Mat. (Kiev) ~ (1971), 77-83. (Zb 228, 65011.)

11. Berkovit2, L.D.; Pollard, H. Addenda to "a variational problem related to an optimal filter problem with self-correlated noise ll

•

Trans. Amer. Math. Soc. 157 (1971), 499-504.

12. Birkhoff, G. The numerical solution of elliptic equations (CBMS Regional Conference Series in Applied Mathematics, no. 1), pp. 55-71. Soc. Indust. Appl. Math., Philadelphia, 1971. (Zb 232, 65068; RJM (1972), 5BI059.)

13. Birkhoff, G. Tricubic polynomial interpolation. Proc. Nat. Acad. Sci. USA 68 (1971), 1162-1164. (RJM (1972), IB1241.)

14. Birkhoff, G.; Priver, A.S. Optimal smoothing of Gaussian periodic data. Indiana Univ. Math. J. 21 (1971), 103-113. (BS 33, 2807.) --

15. Boneva, L.I.; Kendall, D.G.; Stefanov, I. Spline transformations: three new diagnostic aids for the statistical data-analyst. J. Royal Stat. Soc. Sere B II (1971), 1-70.

16. Borzov, V.V. On some applications of piecewise polynomial approximations of functions of anisotropic classes Wr • Dekl. Akad. Nauk SSSR 19~ (1971), 499-501 (Russian). Translated as Soviet Math. Dokl. 12 (1971), 804-807. (MR 44, 701.)

17. Bosarge Jr., W.E.; Johnson, O.G. Error bounds of high order accuracy for the state regulator problem via piecewise polynomial approximations. SIAM J. Control 9 (1971), 15-28. (R~4 (1971), IOB751.)

18. Bosarge Jr., W.E.; Johnson, O.G. Numerical properties of the Ritz-Trefftz algorithm for optimal control. COiron. ACM 14 (1971), 402-406. (Zb 216, p--. 234; RJM (1972), 7B962; CR~, 22180.)

- 50 - 1971

19. Braess, D. Chebyshev approximation by spline functions with free knots. N1..'mer. Math. 17 (1971), 357-366. (Zb 227, 65010; RJM (1972), 3B808; CA~, 620; BS 33, 33.)

20. Bramble, J.H.; Schatz, A.H. On the numerical solution of elliptic boundary value problems by least squares approximation of the data. in~ Numerical solution of partial differential equations II; edt by B.E. Hubbard, pp. 107-131. Acad. Press, New York, 1971. (Y.R 42, 8713; BS ~, 5735.)

21. Bramble, J.H.; Hilbert, S.R. Beunds for a class of linear functionals with applications to Hermite interpolation. Numer. Math. 16 (1971), 362-369. (Zb 214, p. 414; RJM (1971), 8B522; CR 1!, 21738; CA~, 1094; BS 32, 2606.)

22. Bramble, J.H.; Schatz, A.H. Least squares methods for 2mth order elliptic boundary-value problems. Math. Compo 25 (1971), 1-32. (Zb 216, p. 492; RJM (1971), 11BI078; CA~, 1980; BS 32, 6623.)

23. Brauchli, H.J.; aden, J.T.

24.

Conjugate approximation functions in finite-element analysis. Quart. Appl. Math. 29 (1971), 65-90. (lb 226, 65051; RJM-r1972), 8B461; BS 33., 31.)

..,J BrudnYL, Yu.A.

Piecewise polynomial approximation and local approximations. Dokl. Akad. Nauk SSSR 201 (1971), 16-18 (Russian). Tt'anslated as Soviet Math. Dokl. 12 (1971), 1591-1594. (RJM (1972), 3B78; BS 33, 1059.) -

25. Bruvold, N.T. * Optimal and admissible designs for polynomial monospline regression

(Doctoral dissertation). Purdue Univ., Lafayette, 1971. (DA~, 3695-B.)

26. Callenoer, E.D. Single step methods and low order splines for solutions of ordinary differential equations. SIAM J. Numer. Anal. 8 (1971), 61-66. (Zb 219, 65060; RJM (1971), 11BI058; CR~, 22836; CA~, 3202; BS 2~' 5712.) .

27. Canto~i, A. Optimal curve fitting with piecewise linear functions. IEEE Trans. Computers C-~ (1971), 59-67. (CA~, 1 I 3 1. )

28. Cantoni~ A. Improving transient response calculations. Austral. Comput. J. 1 (1971), 156-161. (CR~, 23554.)

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29. Carlson, R.E.; Hall, C.A. On piecewise polynomial interpolation in rectangular polygons. J. Approximation Theory 4 (1971), 37-53. (MR 43, 6628; Zb 206, p.-348; CR~, 22328; BS ~, 4660.)

30. Carlson, R.E.; Hall, C.A. Ritz approximations to two-dimensional boundary value problems. Numer. Math. 18 (1971),171-181. (Zb 21 p. 170; CR Q, 23668; BS 33, 1075.)

31. Cox, M.G.

1971

An algorithm for approximating convex functions by means of first degree splines. Comput. J. 14 (1971), 272-275. (lb 225, 65016; RJM (1972), 3B813; CR Q, 23657; CA~, 2648; BS 33, 26.)

32. Cox, M.G. Curve fitting with piecewise polynomials. J. Inst. Math. Appl. 8 (1971), 36-52. (MR 44, 4870; Zb 219,-65012; RJM (1972), 2B875; BS 33, 22.)

33. Culham, W.E.; Varga, R.S. Numerical methods for time-dependent nonlinear boundary value problems. Soc. Petroleum Engrs. AlME J. ~ (1971), 374-388.

34. Daniel, J.W. The approximate minimization of functionals, pp. 59-65. P~entice Hall, Englewood Cliffs, 1971. (HR 42, 7279; Zb 223, 65014; CR~, 21569.)

35. Daniel, J.W. Convergence of a discretization for constrained spline function problems. SIM~ J. Control 9 (1971), 83-96. (MR 43, 4235; RJM-(1971), IOB805.)

36. Douglas Jr., J.; Dupont, T. Alternating-direction Galerkin methods on rectangles. in: Numerical solution of partial differential equations II; ed. by B.E. Hubbard, p. 133-214. Acad. Press, New York, 1971. (MR 42, 8706.)

.37. Ducateau, Ch. F. Condition pour qu'un pro cede d'interpolation provienne de la minimisa­tion d'une fonction semi-hilbertienne. C.R. Acad. Sci. Paris Ser. A 272 (1971), 266-269. (Mil 42, 8666; Zb 214, p. 424; RJM (1971), 8B497; BS 32, 2600.)

38. Ducateau, Ch.F. * Etude de quelques problemes d'interpolation (These).

Universite de Grenoble, Grenoble, 1971. CBS 32, 5680.)

39. Earnshaw, J.L.; Yuille, I.M. A method of fitting parametric equations for curves and surfaces to sets of points defining them approximately. Computer Aided Design 3 (1971), 19-22. (IlJM (1971), 8B777; BS-32 , 8111.)

- 52 - 1971

40. EinarDson, B. * On the numerical treatment of some integro-differential equations,

Fourier integrals, and integral equations (Doctoral dissertation). Technol. Univ. Stockholm, Stockholm, 1971.

41. El Tom, M.E.A. Application of spline functions to Volterra integral equations. J. lnst. Math. Appl. 8 (1971), 354-357. (Zb 232, 65091; RJM (1972), 7B940; BS 33, 1917.)

42. Fix, G.J.; Larsen, K. Ou the convergence of SOR iterations for finite element approximations to elliptic boundary value problems. SIAM J. Numer. Anal. 8 (1971), 536-547. (kJM (1972), 3B749; BS 33, 1073.)

43. Fyfe, D.J. Linear dependence relations connecting equal interval Nth degree splines and their derivatives. J. lnst. Math. Appl. 7 (1971), 398-406. (MR 44, 1972; Zb 219,-65010; RJM (1972), 3B815; BS 32, 7168.)

44. Gaissmaier, B. Schnelle und genaue Berechnung von Fourierintegralen durch Kombination von Spline-Interpolation und schneller Fourier-Transformation. Nachr.-tech. Z. 24 (1971), 601-60S. (RJM (1972), SBI181; BS 33, 4599.)

45. Golomb, M.; Jerome, J.W. Linear ordinary differential equations with boundary conditions on arbitrary point sets. Trans. Amer. Math. Soc. 153 (1971), 23S-264. (MR 42, 4811; RJM (1971)--, --12B359.)

46. Gordon, W.J. Blending-function methods of bivariate and multivariate interpolation and approximation. SIAM J. Numer. Anal. 8 (1971), 158-177. (MR 43, 8209; RJM (1971), I1BI100; CR~, 21906; CA l1' 3167; BS~, 5673.)

47. Gourlay, A.R. Some recent methods for the numerical solution of time-dependent partial differential equations. Proc. Roy. Soc. London Ser. A 323 (1971), 219-235. (Zb 234, 65080.)

48. Guglielmo, F. di Resolution approchee de problemes aux limites elliptiques par des schemas aux elements finis a plusieurs fonctions arbitraires. Calcolo 8 (1971), 185-213. (KJM (1972). 9B778; CA~, 2738; BS 33, 7060.)

49. Hedstrom, G.W.; Varga, R.S. Application of Besov spaces to spline approximation. J. Approximation Theory 4 (1971), 295-327. (MR 43, 7824; Zb 218, 41001; CR 21, 23962.)

- 53 - 1971

50. Herbold, R.J.; Varga, R.S. The effect of quadrature errors in the numerical solution of two­dimensional boundary value problems by variational techniques. Aequationes Math. 7 (1971), 36-58. (Zb 233, 65056; RiM (1972), 9B781.)

51. Hertling, J. Numerical treatment of singular integral equations by interpolation methods. Nunter. Math. 18 (1971), 101-]12. (RJM (1972), 3B793; CR Q, 23973; CA..!..§., 923; BS 33, ]093.)

52. Hoskins, W.D • . Table for third-degree spline interpolation using equi-spaced knots. Math. Compo 25 (1971), 797-801. (Zb 227, 65009; RJM (1972), 6B931; CA..!..§., 371; BS 33, 2805.)

53. Hulme, B.L. Piecewise polynomial Taylor methods for initial value problems. NU"ller. Math. 17 (1971),367-381. (Zb 209, p. 470; RJM (1972), 3B716; CA..!..§., 640; BS 33, 46.)

54. Ito, T. * A collocation method for boundary value problems using spline functions

(Doctoral dissertation). Brown Univ., Providence, 1971.

55. Jerome, J.W.; Schumaker, L.L. Local bases and computation of g-splines. in: Methoden und Verfahren der mathematischen Physik; hrsg. von B. Brosowski und E. Martensen, Bd 5 (B.I. Hochschulskripten 724a/b), pp. 171-199. Bibliographisches Institut, Mannheim, 1971. (Zb 221, 41010.)

56. Joly, J.L.; Laurent, P.J. Stability and duality in convex minimization problems. Rev. Fran~aise Informat. Recherche Operationnelle ~ (1971), no. R-2, 3-42.

57. Kalik, C. Les fonctionelles generatrices des fonctions splines. Studia Univ. Babe~-Bolyai Ser. Math.-Mech • ..!..§. (1971), no. 1,61-64.

58. Kalik, G. The approximate solution of differential equations.by a class of spline functions (Roumanian). Studia Univ. Babe§-Bolyai Ser. Math.-Mech. 16 (1971), no. 2, 2]-26. (RJM (1972), 4BlI13.)

59. Karlin, S. Total positivity, interpolation by splines, and Green's functions of differential operators. J. Approximation Theory 4 (1971), 91-112. (MR 43, 780; Zb 228, 41002; RJM (1972), 4B827; BS 1£, 4656.)

60. Karlin, S. Best quadrature formulas and splines. J. Approximation Theory 4 (1971), 59-90. (MR 43, 2403; Zb 228, 41004; RJM (1972), 4Bl1S8; CR~, 22195; BS 32, 4678.)·

- 54 - 1971

61. Kennedy, J.W. * Numerical solution of elliptic partial differential equations using

Hermite spaces (Doctoral dissertation). Univ. of Pittsburgh, Pittsburgh, 1971.

62. KersharJl, D. A note on the convergence of interpolatory cubic splines. SIM1 J. Numer. Anal. 8 (1971), 67-74. (MR 43, 7036; Zb 219,-65013; RJM (1971), 12B1183; CA~, 3169; BS 32, 5675.)

63. Kim, Hong-kim * Approximation by spline functions of the solution of hyperbolic equations

(Doctoral dissertation). Univ. of Maryland, College Park, 1971.

64. Kimeldorf, G.; Wahba, G. Some results on Tchebycheffian spline functions. J. Math. Anal. Appl. 33 (1971), 82-95. (~b 185, p. 309; RJM (1971), 9B674; BS 32, 2604.)

65. King, J.T. * Least squares methods for parabolic initial boundary value problems

(Dcctoral dissertation). Cornell Univ., Ithaca, 1971. (DA~, 7433-B.)

66. Knopp, K. Theory and application of infinite series, pp. 518-535. Hafner, New York, 1971.

67. Mangasarian, O.L.; Schumaker, L.L. Discrete splines via mathematical programming. SIAM J. Control 9 (1971), 174-183. (23 223, 65004; RJM (1972), IB1262.)

68. Mansfield, L.E. On the optimal approximation of linear functionals in spaces of bi­variate functions. SIAM J. Numer. Anal. 8 (1971), 115-126. (MR 44, 4873; Zb 219,155024; RJM (1971), 12B1175; CR 12, 21905; BS 32, 5676.) - -

69. Markov & , L.A. The use of properties of spline functions for the solution of the problem on best approximation in certain functional spaces (Russian). Trudy Centro Zonal'n Ob'edin. Mat. Ka£edr. Kalinin. Gos. Mat. Inst. 2 (1971), 101-130. (RJM (1971), 12B1023.)

70. Markova, L.A. Characterization of the elements of best approximation in Hilberc space with the help of splines (Russian). Trudy Centro Zonal'n Ob'edin. Mat. Kafedr. Kalinin. Gos. Mat. lnst. ~ (1971), 131-136.

71. Hicula l G. Forrctions spline d'approximation pour les solutions des systemes d'equations differentielles. Anal. ~tiint. Din Ia§i 17 (1971), no. 1, 139-155. (RJ}1 (1971), 12BI082.)

- 55 - 1971

72. Micula, G. Approximate integration of systems of differential equations by spline functions. StudiaUniv. Babe~-Bolyai Ser. Math.-Mech. ~, no. 2, 27-39. (RJM (1972), 4BII05.)

73. Micula, G. * COl1tributions to the approximate integration of systems of differential

e<;.uations by spline functions (Doctoral dissertation). Univ. of Cluj, Cluj, 1971. i

74. Miranker, W.L. Galerkin approximations and the optimization of difference schemes for bou~dary value problems. SIAM J. Numer. Anal. 8 (1971), 486-496. (RJM (1972), 5B1073j BS ll, 1084.)

75. Mitchell, A.R. The finite element method in partial differential equations. in: Methoden und Verfahren der mathematischen Physik; hrsg. von B. Brosowski und E. Martensen, Bd 5 (B.I. Hochschulskripten 724a/b), pp. 101-115. Bibliographisches Institut, Mannheim, 1971.

76. Mitchell, A.R. Variational principles and the finite-element method in partial differ­ential equations. Pro~. Roy. Soc. London Ser A 323 (1971), 211-217. (Zb 214, p. 419; BS 32, 7217.-)-

77. Morozov, V.A. o~ the approximate solution of operator equations by the method of splines. Do~l. Akad Nauk SSSR 200 (1971). 35-38 (Russian). Tr.anslated as Soviet Math. Dokl. 12 (1971), 1325-1329. (Mil. 44,4546; RJM (1972), IBIOIOjBS 33, 1915.)

78. Morozov, V.A. On the theory of spline functions and the stable computation of the value of an unbounded operator (Russian). Z. Vy~isl. Mat. i Mat. Fiz. II (1971), 545-558. (MR 44, 4545; Zb 229, 65052j-RJM (1971), IOB715; BS 33, 1057.)

79. Murty, V.N. Optimal designs with a Tchebycheffian spline regress10n function. Ann. Math. Statist. 42 (1971), 643-649. (MR 44, 4851.)

80. Murty, V.N. Optimal designs with a polynomial spline regression with a single multiple knot at the center. Ann. Math. Statist. 42 (1971), 952-960. (MR43,7022.) -

81. Naj zar, K. Error bounds for eigenvalues and eigenfunctions of some ordinary differential operators by the method of least squares. Comment. Hath. Univ. Carolinae 12 (1971), 235-248. (Zb 216, p. 490.)

- 56 -

82. Netravali, A.N. * Signal processing techniques based on spline functions (Doctoral

dissertation). Rice Univ., Houston, 1971. (DA 32, 2165-B.)

1971

83. Nitsche, J. Uber ein Variationsprinzip zur Losung von Dirichlet-Problemen bei Ver­wendung von Teilraumen, die keinen Ran~bedingungen unterworfen sind. Abh, Math. Sem. Univ. Hamburg 36 (1971), 9-15. (Zb 229, 65079.) --

84. Okada, Y. A numerical experiment on the fairing of free-form curves. Information Processing in Japan ~ (1969), 69-74.

85. Parlett! B.N.; Johnson, O.G. Numerical implementation of variational methods for eigenvalue problems. in: Mathematical Software; ed. by J.R. Rice, pp. 357-368. Acad. Press, New York, 1971. (CR g, 22822.)

86. Patent, P.D.

87.

* Least square polynomial spline approximations (Doctoral dissertation). California Institute of Technology, Pasadena, 1971.

Petit, M. Unp. propriete des fonctions splines Rev. Fran~aise Informat. Recherche 137-140. (Zb 225, 65015; RJM (1972), 5BI141.)

d'ajustement. Operationnelle 1 (1971), no. R-2,

88. Popov, V.A.; Freud, G. Lower error bounds in the theory of spline approximation (Russian), Studia Sci. Math. Hungar. 6 (1971), 387-391.

89. Prenter, P.M. Piecewise L-splines. Numer. Math. 18 (1971), 243-253. (Zb 227, 65012; RJM (1972), 6B810; CR g, 23818; CA~, 1189; BS 33, 1890.)

90. Reid, J.K. A note on the approximation of plane regions. Compo J. 14 (1971), 307-308. (Zb 224, 65004; CR g, 22474; BS 33, 25.)

91. Reinsch, C.R. Smoothing by spline functions. II. Nu~er. Math. 16 (1971), 451-454. (RJM (1971), 6B928; CR~, 21904; CA~, 2359; BS 32, 3465.)

92. Richter--Dyn, N. Minimal interpolation and approximation in Hilbert spaces. SIAM J. Numer. Anal. 8 (1971), 583-597. (Zb 229, 65016; RJM (1972), 6B808; CR g, 23659; BS 33, 1050.)

93. Rosen, J.B. ~linimum error bounds for multidimensional spline approximation. J. Comput. System Sci. 5 (1971), 430-452. (MR 44, 693; Zb 231, 65013; RJM (1972), 7B956; CA~, 2907.)

- 57 - 1971

94. Rosen, J.B.; LaFata, P.S. Interactive graphical spline approximation to boundary value problems. Proc. ACM 1971, Annual Conf., pp. 466-481. Assoc. Compo Mach., New York, 1971. (CR~, 22324.)

95. Sakai, M, Piecewise cubic interpolation and two-point boundary value problems. Publ. Res. Inst. Math. Sci. I (1971), 345-362. (RJM (1972), 8B852.)

96. Sard, A.; Weintraub, S. * A book of splines.

Wiley, New York, 1971. (MR ±i, 1191; Zb 232, 65003; RJM (1972), 3B811.)

97. Schechter, E. A piecewise Lagrange interpolation with application to error estimates in finite-difference methods. Studia Univ. Babe~-Bolyai Sere Math.-Mech. 16 (1971), no. 2, 67-73. (RJM (1972), 4Bll 12.)

98. Schoenherg, I.J. On equidistant cubic spline interpolation. Bull. Amer. Math. Soc. 77 (1971), 1039-1044. (MR 43, 7819; RJM (1972~ 6B930.)

99. Schoenberg, I.J. The perfect B-splines and a time-optimal control problem. Israel J. Math. 10 (1971), 261-274. (RJM (1972), 7B827.)

100. Schoenberg, I.J.; Sharma, A. The interpolatory background of the Euler-Maclaurin quadrature formula. Bull. Amer.Math. Soc. 77 (1971), 1034-1038. (MR 44, 4446; RJM (1972~ 6B916.)

101. Schult2, M.H. L2 error bounds for the Rayleigh-Ritz-Galerkin method. SIAM J. Numer. Anal. 8 (1971), 737-748. (RJM (1972), 7B912; BS ~, 2839.)

102. Serbin, S.M. * A computational investigation of least squares and other projection

methods for the approximate solution of boundary value problems (Doctoral dissertation). Cornell Univ., Ithaca, 1971. (DA~, 7179-B.)

103. Silliman, S.D. * The numerical evaluation by splines of the Fourier transform and the

Laplace transform (Doctoral dissertation). Univ. of Wisconsin, Madison, 1971. (eA~, 4743-B.)

104. Smith, C.L. * A direct method approximation to the linear parabolic regulator control

problem using multivariate splines (Doctoral dissertation). Rice Univ., Houston, 1971. (DA~, 2296-B.)

- 58 -

105. Smith, P.W. * Wr'P-splines (Doctoral dissertation).

Purdue Dniv., Lafayette, 1971.

106. Spath, H. Algorithm 16. Two-dimensional exponential splines. Computing 7 (1971), 364-369. (Zb 226, 65006; RJM (1972), 3B817; CA~, 2924.)

107. Spath, H.

1971

Die numerische Berechnung von interpolierenden Spline-Funktionen mit Blockunterrelaxation. . Z. Angew. Math. Mech. 51 (1971), Sonderheft, T73. (Zb 217, p. 522.)

108. Spath, H. Berichtigung zu Algorithmus 10. Computing 8 (1971), 200-201. (CA.!.§., 384.)

109. Spath, H. The numerical calculation of high degree Lidstone splines with equI­distant knots by blockunderrelaxation. Computing 7 (1971), 65-74. (Zb 215. p~ 272; CA~, 1986; BS 32, 8108.)

110. Spath, H. The numerical calculation of quintic splines by blockunderrelaxation. Computing 7 (1971), 75-82. (Zb 216, p~ 230; RJM (197]), 12B1178; CA~, 1987; BS~, 8109.)

III. Spath, H. Rationale Spline-InterpolaLion. Angew. lnformatik 13 (1971), 357-359. (CA.!.§., 2485; BS 32, 7170.)

112. Strang, G. The finite element method and approximation theory. in: Numerical solution of partial differential equations II; ed. by B.E. Hubbard, pp. 547-583. Acad. Press, New York, 1971. (MR 44, 4926; BS~, 5739.)

112a. Studden, W.J. Optimal designs and spline regression. in: Optimizing methods in statistics (Proe. Symp. Ohio State Dniv., June 1971); ed. by J.S. Rustagi, pp. 63-76. Acad. Press, New York, 1971.

113. Subbotin, Yu.N. A relation between spline approximation and the problem of the approxI­mation of one class by another. Mat. Zametki 9 (1971), 501-510 (Russian). Translated as-Hath. Notes 9 (1971), 289-294. (Zb 218, 41003; RJN (1971):- 8B74; BS 32, 7156.)

114. Subbotin, Yu.N. Approximation by spline functions and estimates of diameters (Russian). Trudy Mat. Inst. Steklov 109 (1971), 35-60. (RJN (1972), 3B71; BS~, 2816.) .

1 IS. Takagi, S. Numerical differentiation by spline functions applied to a lake temperature observation. J.Computational Phys. 8 (1971), 285-291. (CA 15, 3227.) -

- 59 -

1 16. Tihomirov, V. M. Some problems in approximation theory. Mat. Zametki 9 (1971), 593-607 (Russian). Translated as-Math. Notes 2. (197J), 343-350.

117. Varga, R.S.

1971

Some results in approximation theory with applications to numerical analysis. in: Numerical solution of partial differential equations II; ed. by B.E. Hubbard, pp. 623-649. Acad. Press, New York, 1971. (BS E., 5756.)

118. Varga, R.S. * Functional analysis and approximation theory in numerical analysis

(CBMS Regional Conference Series in Applied Mathematics, no. 3). Soc. Indust. Appl. Math., Philadelphia, 1971. (Zb 226, 65064; RJM (1972), 5B97J.)

119. Velikia, V.L.; Korne~ruk, N.P. Accurate estimates of deviations of spline approximations to classes of differentiable functions. Mat. Zametki 9 (1971), 483-494 (Russian). Translated as-Math. Notes 9 (1971), 278-284. (Zb 216, p. 589; RJM (1971), 8B80; BS E., 7155.)

120. Voss, D.A. * A spline shooting technique for two point boundary value problems

(Doctoral dissertation). Iowa State Univ., Iowa City, 1971. (DA 32, 2298-B.)

1 2 1. Wahba, G. A polynomial algorithm for density estimation. Ann. Math. Statist. 42 (1971), 1870-1886.

122. Wahba,G. On the regression design problem of Sacks and Ylvisaker. P_nn. Math. Statist. 42 (1971), 1035-1053. (MR 43, 5676.) -

123. Walter, H. * Numerische Darstellung von Oberflachen under Verwendung eines Optimal­

prinzips (Dissertation). T~chnische Universitat Munchen, Munchen, 1971. (RJM (1972), 5BI167.)

124. Whiten, Iv.J. The use of multi-dimensional cubic spline functions for regression and smoothing. Austral. Comput. J. 3 (1971), 81-88. (MR 44, 3466; Zb 226~ 65009.)

125. Widlund, O.B. Some results on best possible error bounds for finite element methods and approximation with piecewise polynomial functions. in: Conference on applications of numerical analysis (Lecture notes in mathematics, no. 228), pp. 253-263. Springer Verlag, Berlin, 1971. (Zb 234, 65091; RJM (1972),5B1076; BS ll. 56.)

- 60 -

126. Young, J.D. Smoothing data with tolerances by use of linear programming. J. lnst. Math. Appl. ~ (1971), 69-79. (BS 33, 24.)

127. Young, J.D. The space of cubic splines with specified knots. The Logistics Review 7 (1971), no. 30, 3-8. (RJM (1971), IIBI101.)

128. Young, J.D.

1971

Numerical solution of nonlinear second order ordinary differential equations by use of cubic splines. Tb.e Logistics Review 7 (1971), no. 33, 5-18. (rJM (1972), 9B768.) -

129. Zafarullah, A. Spline functions as approximate solutions of boundary-value problems. J. Optimization Theory Appl. 7 (1971), 178-188. (MR 43, 7082; RJM (1971), 10B756.)

- 61 -

Index of authors

The names of the authors of the enlisted publications are given here in

alphabetical order, together with a coded list of their papers. The meaning

of the cumpound numbers used as abbreviations of the papers is simply as

follows: the symbol 62-5, for instance, refers to a publication that appeared

in 1962 and has number 5 under that heading in the bibliography.

Ahlberg, J.R.

Ahlin, A. C.

Ahuj a, D. V.

Akima, Ii.

Albasiny, E.L.

Amos, D" E.

Amunruc:., L.R.

Anderssen, A.S.

Anselone, P.M.

Asker, B.

Atkins, r:.A.

Atkinson, K.E.

Atteia" M.

Aubin, J.P.

Bacopoulos, A.

Barnhill, R. E.

Barrar, R.B.

Barrodale, I.

Bavinck, H.

Bedau, K.D.

Bellman, R.

Belov, Yu.A.

Bel'tjukov, B.A.

Berger, S.A.

Berkovitz, 1.D.

Bhattacharyya, B.K.

(62-5; 63-1; 64-1; 65-1,2,3,4; 66-1; 67-1,2; 68-1;

69-1,2; 70-1,2; 71-1)

(64-2)

(68-2,3)

(70-3)

(69-3; 71-2)

(69-4)

(68-4)

(71-3)

(68-5)

(62-1)

(66-6)

(68-6)

(65-5,6; 66-2,3; 67-3,4; 68-7; 70-4; 71-4)

(66-4; 67-5,6; 68-8,9; 71-5,6)

(71-7)

(69-5)

(70-5)

(66-5)

(71-8)

(69-6)

(69-7; 71-9)

(71-10)

(67-7)

(63-2; 66-6)

(67-8; 69-8; 70-6; 71-11)

(69-9)

Bickley, W. G.

Birkhoff, G.

Birman, M.~.

Blue, J.L.

Boneva~ L.1.

Boor C. I{. de

Borzov, V.V.

Bosarge Jr., W.E.

Braess, D.

Bramble, J.H.

Brauchli, H.J. ~ Brudnyl., Yu.A.

Bruvold, N.T.

Buchanan, J.E.

Bulirsch, R.

Burchard, H.G.

Callendl;!r, E.D.

Cantoni, A.

Carasso, C.

Carlson, R.E.

Case, j.R.

Cavar~tta Jr., A.S.

Cavendish, J.C.

Chan, P.P.-Y.

Cheney, E.W.

Chernykh, N.1.

Cherruault, Y.

Chi, D.N.-H.

Chu, S.C.

Ciarlet, P.G.

Ciesielski, z. Coatmelec, C.

Collatz, L.

Coons, S.A.

Covaci-Munteanu, M.J.

- 62 -

(68-10; 69-10)

(60-1; 64-3; 65-7; 66-7; 67-9,10; 68-11,12; 69-11,12;

70-7; 71-12,13,14)

(66-8; 67-11)

(69-13)

(71-15)

(62-2; 63-3; 64-3; 65-7; 66-7,9,10; 68-13,14,15; 69-14)

(71-16)

(70-8; 71-17,18)

(71-19)

(70-9,10; 71-20,21,22)

(71-23)

(61-1; 63-4; 71-24)

(71-25)

(68-16)

(68-17)

(71-6)

(71-26)

(71-27,28)

(66-11; 67-12,13,14,15,16,17; 69-15)

(71-29,30)

(70-11)

(70-12)

(68-18; 69-16)

(70-13)

(68-19,62; 70-14,15)

(70-107)

(68-20)

(70-16)

(70- 17,56)

(66-12; 67-18; 68-21,22,23,24,25; 69-17; 70-18,19)

(59-1,2; 60-2,3; 63-5; 64-4; 66-13; 68-26; 69-18)

(66-14,15)

(38-1; 65-8)

(68-3)

(70-20)

Cox, M.C.

Culham. W.E.

Curry, H.B.

Curtis, A.R.

Cybertowicz, Z.

Dailey, J.W.

Daniel, J.W.

Delvos, F.J.

Denman, H.H.

Diringer, P.

Dobysh, A.D.

Douglas Jr., J.

Ducateau, Ch.F.

Dupont, T.

Earnsha-N', J.L.

Eastman, W.L.

Ehlich, H.

Einarsson, B.

Elhay, S.

El Tom, M.E.A. .. " Ermusa, A.E.

Esch, R.E.

Favard, J.

,Ferguson, J.

Ferrand, C.

Fitzgerald, C.H.

Fitzgerald, J.M.

Fix, G.J.

Forrest, A.R.

Freeman, H.

Freud, G.

Fyfe, D.J.

Gaier, D.

Gaissmaier, B.

Galkin, P.V.

(71-31,32)

(71-33)

(66-16)

- 63 -

(70-21 )

(67-19; 68-27)

(69-19)

(71-34,35)

(70-22)

(64-9; 69-20)

(68-28)

(70-23,24 )

(70-25; 7I -36)

(68-29; 70-26; 71-37,38)

(70-25; 71-36)

(71-39)

(69-23)

(66-]7)

(68-30; 69-21; 71-40)

(69-22)

(68-3 1; 7 1-4 ) )

(68-39)

(69-23)

(40-) )

(64-5)

(67-20)

(69-24)

(70-27)

(68-32; 69-25,26; 70-7; 71-42)

(68-33)

(69-27)

(70-28; 71-88)

(69-28; 70-29; 71-43)

(70-30)

(71-44)

(70-31 )

Garabedian, H.L.

Gautschi, W.

Gerald, C.F.

Glass, J.M.

Gold, S.G.

Golomb, M.

Gopengauz, I.E.

Gordon) W.J.

Gourlay! A.R.

Greville, T.N.E.

Griffiths B.A.

Guglielmo, F. di

Haimovid, A.

Hall, C. P .•

HammerHn, G.

Handscomb, D.C.

HaussmaIL, W.

Hayes, J.G.

Hedstrom, G.W.

Heindl. G,

Herbold, R.J.

Hertling, J.

Hilbert, S.R.

Hill, 1. D.

Holladay, J.e.

Hori, S.

Horsley, A.

Hosaka, M.

Hoskins, W.D.

Hulme, B.L.

Hung, H.-S.

Ikaunieks, E.A.

Innanen, K.A.

Ionescu, n.v. Ito, T.

(60-1 )

(71-8)

(70-32)

- 64 -

(65-9; 66-18; 69-27)

(70-33)

(59~3; 68-34; 69-29; 71-45)

(61-1; 63-4)

(68-12; 69-30,31; 71-46)

(71-47)

(64-6; 67-21,22; 69-32,33; 70-34)

(49-3)

(69-34; 70-35; 71-48)

(70-36)

(68-35; 69-35,36; 7i-29,30)

(70-37)

(66-19,20,21; 70-38)

(70-39)

(70-40)

(71-49)

(69.,.37)

(68-36; 69-38,39; 71-50)

(70-41; 71-51)

(69-40; 70-9; 71-21)

(69-41)

(57-I )

(70-105)

(68-37)

(69-42)

(69-3; 70-42; 71-2,52)

(68-38; 69-43; 71-53)

(70-43)

(68-39)

(66-22)

(57-2; 70-44,45)

(71-54)

Janenko, N.N.

Jerome, J.W.

Johnson, O.G.

Johnson~ R.S.

Joly, J.L.

Kalik, c. Karlin, S.

Karon, J.M.

Kautsky, J.

Kendall, D.G.

Kennedy, J.W.

Kershaw, D.

Khazankina, N.P.

Kim, Hong-Kim

Kimeldorf, G.S.

King, J.T.

Kirishchiev, R.I.

Knopp, K.

"" Korne~cuk, N.P.

KrinzeGza, F.

Krylov, V. 1.

Kvasov, B.I.

LaFata, P.S.

Landis, F.

Langhaar, H.L.

Langner, W.

Larkin, W.J.

Larsen, K.

Lathrop, J.F.

Laurent, P.J.

Lee, J.W.

Levina, pi.

Lipow, P.R.

Little, R.N.

Loeb, H.L.

- 65 -

(70-46,47)

(68-40; 69-44,45,46; 70-48; 71-45,55)

(68-41; 69-47; 70-8; 71-17,18,85)

(60-4)

(67-23,24; 71-56)

(70-49; 71-57,58)

(66-23,24; 67-25,26; 68-42,43; 69-48,49; 70-50,51;

71-59,60)

(68-43,44; 69-50; 70-50)

(70-52)

(71-15)

(71-61)

(69-51;71-62)

(68-52; 69-72)

(71-63)

(70-53,54; 71-64)

(71-65)

(65-10)

(71-66)

(69-52; 71-119)

(69-53)

(59-4)

(70-46,47)

(70-55; 71-94)

(62-3)

(70-56)

(70-57)

(69-20)

(71-42)

(69-54)

(68-5,45,46; 69-15,55; 71-56)

(69-56; 70-51)

(70-58,59)

(70-60)

(70-105)

(70-5)

Loginov, A.S.

Loscalzo~ F.R.

Love, A.E.H.

Lucas, T.R. ... v Luspal., N.E.

Lynch, R.E.

Mahto, K.R.

Malozemov, V. N.

Mangasarian, O.L.

Mann, W.R.

Mansfield, L.E.

Markova, L.A.

Marsaglia, G.

Marsden, M.J.

Maruashvili, T.I.

McClure, D.E.

McConalogue, D.J.

Mehlum, E.

Meinguet, J.

Meir, A..

MeyerG, L.F.

Micula s G.

Mil ne s, H. W.

Miranker. W.L.

Mishra, B.N.

Mi tchell, A. R.

Moler, C.B.

Moriu, M.

Morozov, V.A.

Munteanu, M.J.

Murty, '1. N.

Musielak, J.

Najzar, K.

Nattere1.:', F.

Neshevich, D.A.

Netravali, A.N.

- 66 -

(69-57 ;70-6)

(67-27,28; 68-47; 69-58)

(44-1)

(70-62,63)

(69-52)

(66-10)

(70-69)

(66-25; 67-29)

(69-59; 71-67)

(70-105)

(69-60; 71-68)

(71-69,70)

(70-64)

(66-26; 68-48; 70-65; 71-7)

(69-61)

(70-66)

(70--67)

(64-7; 69-62)

(67-30; 70-68)

(66-33; 68-49,50; 69-63,103)

(50-1,2)

(71-71,72,73)

(66-27)

(71-74)

(70-69)

(71-75,76)

(70-70)

(69-64)

(70-71; 71-77,78)

(68-51 )

(69-65; 71-79,80)

(59-1 )

(71-81)

(69-66; 70-19,72)

(65-10)

(7) -82)

Nielson, G.M.

Nikolskit, S.M.

Nilson, E.N.

Nitsche, J.

Nord, S.

Oden, J.T.

Okada, y,

Ostapenko, V.N.

Parker, J.B.

Parker, K.

Parlett, B.N.

Patent, P.D.

P., oil • ava 01.U, I.

Pereyra, V.

Perrin, F.M.

Petersen, 1.

Petit, M.

Phillips, G.M.

Pierce~ J.G.

Podolsky, B.

Pollard, H.

Popov, V.A.

Popoviciu, T.

Powell, M.J .D.

Prente:r, P.M.

Price, H.S.

Price, J.A.

Price, K.H.

Priver, A.S.

Quade, W.

Reid, .T.K.

Reinsch, C.H.

Rice, J.R.

Richards, F.B.

(70-73)

(58-1 )

- 67 -

(62-3,5; 63-1; 64-1; 65-1,2,3,4; 66-1; 67-1,2; 68-1;

69-1; 70-2,74; 7)-])

(69-67,68,69,70,71; 70-75,76; 71-83)

(67-31)

(71-23)

(71-84 )

(68-52; 69-72)

(68-37 ; 70-77)

(68-37; 70-78)

(71-85)

(71-86)

(64-8)

(70-79)

(67-32; 69-73)

(62-4)

(71-87)

(68-53)

(69-74)

(64-9)

(67-8; 69-8; 70-6; 71-11)

(70-28,80,103; 71-88)

(41-1)

(68-54; 69-75,76; 70-81)

(71-89)

(68-18; 69-16,73; 70-82)

(68-37)

(70-15)

(67-10; 70-83; 71-14)

(38- I)

(71-90)

(67-33; 71-91)

(67-34; 69-77,78,79; 70-84)

(70-85)

Richter--Uyu. N.

Ritter, K.

Rivlin, T.J.

Rosen, J.B,

Rosman, :a.H. Roth, R.S.

Runge, c. Russell, R .. D.

Rutishauser, H.

Sakai, M.

Sale, A.H.J.

Sard, A.

Schaback, R.

Schaefer, H.

Schatz, A~H.

Schechter" E.

Schempp, W.

Scherer, K.

Schoenberg, I.J.

Schonefeld, S.A.

Schultz, M.H.

Schumaker, L.L.

Schurer J F.

Schweikert, D.G.

Schwerdtfeger, H.

Secrest, D.

Sendov, B.H.

Serbin, S.M.

Shah, J.M. -.I

Sha~daF..va, T.A.

Sharma, A.

Shchedvin, B.M.

- 68 -

(71-92)

(69-80,81; 70-86)

(E9-82)

(70-55; 71-93,94)

, (70-87)

(69-7; 71-9)

(O!~-1 )

(70-88)

(60-5 ;68- I 7)

(69-83; 70-89,90; 71-95)

(70-91)

(49~1; 50-1,2; 63-6; 67-35; 68-55; 71-96)

(69-84)

(63-7)

(70-10; 71-20,22)

(64-10; 70-92; 71-97)

(70-22,93,94)

," (70-95)

(46-1,2; 49-2; 53-1; 58-2; 64-11,12,13,14,15,16; 65-11;

66-16,26,28,29; 67-36; 68-56,57,58; 69-85,86,87,88;

70-96,97,98; 71-98,99,100)

(69-89,90)

(67-18,37; 68-11,22,23,24,25; 69-17,38,39,91,92,93,94,

95,96,97,98,99; 70-99,100,101; 71-101)

(66-30; 67-25; 68-40,59,60; 69-24,45,46,59,100,101,102;

71-55,67)

(68-19,61,62; 70-14,i02)

(66-31,32)

(60"'-6; 61-2)

(65-12,13,14)

(70-80, 103)

(71-102)

(70-104)

(54-I; 59-5)

(66-33; 68-49,50; 69-63 j I03; 71-100)

(70-118)

Shisha~ O.

Shu, H.

Silliman, S.D.

Simonsen, W.

Simpson, R.B.

Sims, S.E.

Slater, M.L.

Smirnov, V.M.

Smith, C.L.

Smith, P.W.

Smoluk, A.

Sokolnikoff, I.S.

Solomj ak, M. Z.

Solomon, L.P.

Sonneveld, P.

Spath, H.

Starkweather, W.

Stefanov, 1.

Stephens, A.B.

Stern, M.D.

Storchai, V.F.

Stra.ng, G.

Studden, W.J.

Subbotin, Yu.N.

Swartz, B.K.

Synge, J.L.

Takagi, S.

Talbot, T.D.

Tapia, R.A.

Terekhov, T.S.

Theilheimer, F.

Thomann, J.

Thomas, D.H.

Tiholuirov, V.~1.

(68-63)

(70-105 )

(71-103)

(59-6)

- 69 -

(68-64; 69-104)

(69-105)

(69-4)

(68-65)

(71-104)

(71-105)

(64-17; 67-38,39)

(56-1 )

(66-8; 67-11)

(70-70)

(69-106)

(68-66; 69-107, 108, 109, 110, 11 1; 71-106, 107, 108, 109, I 10, 1 I 1 )

(61-3)

(71-15)

(69-112)

(66-34; 67-40)

(69-113)

(69-26; 71-112)

(66-23; 69-114; 71-112a)

(65-15; 67-41,42; 69-115; 70-106,107,108,109,110;

71-113,114)

(66-7; 68-67; 69-116; 70-111)

(49-3)

(71-115)

(67-27,28)

(66-6)

(70-112)

(61-3)

(70-1 13, 114)

(68-16)

(65-16; 69-117;70-115; 71-116)

Van Arman, D.J.

Varga, N.S.

Veedeneev, E.P.

Velikin., V.L.

Voss, D.A •.

Wahba, G.

Wakoff, G.1.

Walsh, J.L.

Walter, H.

Webster, W.C.

Weinberger, H.F.

Weintr aub, S.

Wend:-off, B.

White, E.T.

Whiten, W.J.

Whitney, A.

Widlund, a.B. Willem&, G.M.

Wirtinger, w. Wixom, J.A.

Woodford, C.H.

Young, A.

Young, J.D.

Yuille J I.M.

Zafarullah, A.

Zavjalov, Yu.S.

Zhensykbaev, A.A.

ZhidkoV', N.P.

Ziegler, z.

- 70 -

(68-68; 69-114)

(66-35; 67-18,37; 68-11,18,22,23,24,25; 69-16,17,38,39,

44,73,118; 70-18,19,82,116,117; 71-33,49,50,tI7,118)

(70-118)

(70-119,120; 71-119}

(71-120)

(70-53,54; 71-64,121,122)

(69-119)

(62-5; 64-1; 65-1,2,4; 67-1,2; 68-1; 69-1; 71-1)

(71-123)

(63-2; 66-6)

(59-3; 61-4)

(71-96)

(65-17; 66-7; 69-116,120)

(71-3)

(71-124)

(49-2; 53-I)

(71-125)

(71-8)

(02- I)

(69-5)

(69-121; 70-121)

(66-5)

(67-43; 68-69,70; 69~]22; 70-122,123; 71-126,127,128)

(70-124; 71-39)

(70-125; 71-129)

(69-123; 70-126,127,128,129,130)

(70-120)

(70-118)

(66-24; 67-26; 69-124; 70-97)