Let p = [a, b] be the root of ƒ € C¹([a, b]), and assume f'(p) = f'(po) for some po € [a, b]. Consider an iteration scheme that is similar to, but different from Newton's method: given po, define Pn+1 = Pn f (Pn) f'(po)' n ≥ 0. Assuming that the iterative scheme converges, i.e. that pn → p as n → ∞, show that this method has order of convergence a = = 1.

Let p = [a, b] be the root of ƒ € C¹([a, b]), and assume f'(p) = f'(po) for some po € [a, b]. Consider an iteration scheme that is similar to, but different from Newton's method: given po, define Pn+1 = Pn f (Pn) f'(po)' n ≥ 0. Assuming that the iterative scheme converges, i.e. that pn → p as n → ∞, show that this method has order of convergence a = = 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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