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Math / Numerical Analysis 9 / Chapter 2.2 / Problem 22

Numerical Analysis | 9th Edition | ISBN: 9780538733519 | Authors: Richard L. Burden, J. Douglas Faires

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Answer: Suppose that g is continuously differentiable on some interval (c, d) that

Chapter 2, Problem 22

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QUESTION:

Suppose that g is continuously differentiable on some interval (c, d) that contains the fixed point p of g. Show that if |g ( p)| < 1, then there exists a > 0 such that if |p0 p| , then the fixed-point iteration converges.

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QUESTION:

Suppose that g is continuously differentiable on some interval (c, d) that contains the fixed point p of g. Show that if |g ( p)| < 1, then there exists a > 0 such that if |p0 p| , then the fixed-point iteration converges.

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Step 1 of 3

For a given , there exist a real number such that for implies that more over,

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