7.1 naïve gaussian elimination 8.1 the lu factorization
TRANSCRIPT
7.1 Naïve Gaussian Elimination8.1 The LU Factorization
• Motivating Ax=b: Newton's method for systems of nonlinear equations (pp. 96-99) • C&K 7.1: Naive Gaussian Elimination
– See answered problems (1, 2, 3ab, 4, 5, 6, 7abc)
• C&K 8.1: Matrix Factorizations (see pp. 293-302 on LU factorization)– See answered problems (1-8)
A x = b
Motivation: Newton’s Method (for systems of nonlinear equations, pp.96-99)
Motivation: Newton’s Method (for systems of nonlinear equations, pp.96-99)
Motivation: Newton’s Method (for systems of nonlinear equations, pp.96-99)
Example 2 (p. 99)
Cha
pter
7.1
(p.
245
)
A x = b
A x = b
A x = b
Naïve Gaussian Elimination
Naïve Gaussian Elimination
Naïve Gaussian Elimination
Naïve Gaussian Elimination
Back Substitution
Naïve Gaussian Elimination
Naïve Gaussian Elimination
Naïve Gaussian Elimination
Continuing to second equation…
kth step of forward elimination
Naïve GE: Pseudocode
Storing Multipliers (instead of zeros)
Back Substitution
Back Substitution
Back Substitution
LU Factorization Example(supplements chalkboard)
Matrix Interpretation
Column 1
Column 2
Column 3
Recognizing “L”
Verifying LU=A