2.Giveng(x) = 4x – -Prove that the given form a =for the use of fixed point iteration method. Thus, use the fixed pointiteration formula x41 = 9(x,) to find the root starting with ro = 3.2.Stop the iteration when |a+1 - *,| < 0.005.g(x) satisfies the convergence criteria%3D

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Answered: 2. Given 9(z) = 4x- Prove that the…

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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Consider the Fixed Point iteration algorithm defined by the formula za+1 = 9(In), where g(z) = I- a+ 2ae. Here a eR is a parameter. (a) Find the fixed point, p. (b) Does there exist a value of a for which the iterations could converge quadratically? If yes, find it and explain your answer.
4
Here are three different g(x) functions. All are rearrangements of the same f(x). g(x) 4+ 2.x3 - 2x x2 g(x) = /: 4 16 + x³ • g(x) g(x) = 5x2 (a) What is f()? (b) Are there starting values for which one or more of these converge or diverge?
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2. Given 9(z) = 4x- Prove that the given form r g(x) satisfies the convergence criteria for the use of fixed point iteration method. Thus, use the fixed point iteration formula Ii+1 = 9(x;) to find the root starting with ro = 3.2. Stop the iteration when |r+1-r| < 0.005.