Numerical Analysis
Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 11.3, Problem 9ES

Prove Theorem 11.3. [Hint: To use Theorem 6.31, first show that | h 2 (xi)| < 1 implies that | 1 h 2 p ( x i ) | + | 1 + h 2 p ( x i ) | = 2. ]

Theorem 11.3 Suppose that p, q, and r are continuous on [a, b]. If q(x) ≥ 0 on [a, b], then the tridiagonal linear system (11.19) has a unique solution provided that h < 2/L, where L = maxa xb |p(x)|.

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