05.05.1

Chapter 05.05 Spline Method of Interpolation 1. The following n data points, ( )11, yx , ( )22 , yx , .. ( )nn yx , , are given. For

conducting quadratic spline interpolation the x -data needs to be (A) equally spaced (B) placed in ascending or descending order of x -values (C) integers (D) positive

2. In cubic spline interpolation,(A) the first derivatives of the splines are continuous at the interior data points (B) the second derivatives of the splines are continuous at the interior data

points (C) the first and the second derivatives of the splines are continuous at the

interior data points (D) the third derivatives of the splines are continuous at the interior data points

3. The following incomplete y vs. x data is given.x 1 2 4 6 7 y 5 11 ???? ???? 32

The data is fit by quadratic spline interpolants given by ( ) 1= axxf , 21 x( ) 42 ,9142 2 += xxxxf( ) 64 ,2 ++= xdcxbxxf( ) 76 ,92830325 2 += xxxxf

where dcba and ,,, are constants. The value of c is most nearly (A) 00.303 (B) 50.144 (C) 0.0000 (D) 14.000

4. The following incomplete y vs. x data is given.x 1 2 4 6 7 y 5 11 ???? ???? 32

The data is fit by quadratic spline interpolants given by f (x) = ax 1, 1 x 2 ,f (x) = 2x2 +14x 9, 2 x 4f (x) = bx2 + cx + d , 4 x 6f (x) = ex2 + fx + g, 6 x 7

where a, b, c, d , e, f , and g are constants. The value of dxdf at x = 2.6 most nearly is

(A) 144.50 (B) 4.0000 (C) 3.6000 (D) 12.200

05.05.2 Chapter 05.05

5. The following incomplete y vs. x data is given.x 1 2 4 6 7 y 5 11 ???? ???? 32

The data is fit by quadratic spline interpolants given by ( ) 21 ,1 = xaxxf ,( ) 42 ,9142 2 += xxxxf( ) 64 ,2 ++= xdcxbxxf( ) 76 ,92830325 2 += xxxxf

where dcba and ,,, are constants. What is the value of ( )5.3

5.1

dxxf ?

(A) 23.500 (B) 25.667 (C) 25.750 (D) 28.000

6. A robot needs to follow a path that passes consecutively through six points as shownin the figure. To find the shortest path that is also smooth you would recommendwhich of the following?

(A) Pass a fifth order polynomial through the data (B) Pass linear splines through the data (C) Pass quadratic splines through the data (D) Regress the data to a second order polynomial

Path of a Robot

0

2

4

6

8

0 5 10 15

x

y

quiz_05inp_backgroundMultiple-Choice TestChapter 05.01Background on Interpolationquiz_05inp_directMultiple-Choice TestChapter 05.02Direct Method of Interpolationquiz_05inp_lagrangeMultiple-Choice TestChapter 05.04Lagrange Method of Interpolationquiz_05inp_splineMultiple-Choice TestChapter 05.05Spline Method of Interpolation

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