32. Derive the error formula for Newton's methodM2|f'(Pn)|assuming the hypothesis of Theorem 2.6 hold, that f'(pn) #0, andM = max |f"(x)|. [Hint: Use the Taylor polynomial as in the derivation of Newton'sMethod in the beginning of this section.]P - Pn+| ≤-|P - Pn|²

To Derive: Error formula for Newton's method pn+1-p≤pn-p2M2f'(pn) where M=maxf''(x).

Answered: 2. Derive the error formula for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Derive the error formula for Newton's method |P - Pn+| ≤ M - p - Pn|² 2|f'(Pn)| assuming the hypothesis of Theorem 2.6 hold, that f'(Pn) #0, and M = max|f"(x) [Hint: Use the Taylor polynomial as in the derivation of Newton's Method in the beginning of this section.]