f' (y) # 0 and |p – y| is "small" (e.g. |p – y| < 0). Derive Newton's method starting with th fırst Taylor polynomial for f (x) expanded about y.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 11EQ
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Suppose that f E C² [a, b]. Let y E [a, b] be an approximation to root p such that
Transcribed Image Text:Suppose that f E C² [a, b]. Let y E [a, b] be an approximation to root p such that
f' (y) + 0 and p – y| is "small" (e.g. p – y| < 0). Derive Newton's method starting with the
fırst Taylor polynomial for f (x) expanded about y.
Transcribed Image Text:f' (y) + 0 and p – y| is "small" (e.g. p – y| < 0). Derive Newton's method starting with the fırst Taylor polynomial for f (x) expanded about y.
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