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
Related questions
Question

Transcribed Image Text: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-1
Xn-1 Xn-2
9
g' (p)
(b) |en| ~₁ |In — Xn-1|-
g' (p)-1
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 10 images

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

