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.
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.
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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