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.

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.

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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Question

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.

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