Suppose that the sequence {n} is generated by the fixed point iteration method xn = g(xn-1),n ≥ 1. Further, suppose that the sequence convergence linearly to the fixed point p. Show that(a) g'(p) ~ _In-n-1Xn-1 Xn-29g' (p)(b) |en| ~₁ |In — Xn-1|-g' (p)-1

(A) Let,then from fixed point iteration method , As sequence converges linearly ,then neglecting…

Answered: Suppose that the sequence {x} is…

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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Suppose that the sequence {x} is generated by the fixed point iteration method în = g(xn-1), n ≥ 1. Further, suppose that the sequence convergence linearly to the fixed point p. Show that (a) g'(p) ~ (b) en Xn-In-1 xn-1-Xn-2' g'(p) g'(p)-1 |xn - xn-11.