(1) Consider the Fixed Point iteration algorithm defined by the formula rn+1 = g(xn), where g(x): x - a+ 2ae. Here a E R is a parameter. %3D (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.

(1) Consider the Fixed Point iteration algorithm defined by the formula rn+1 = g(xn), where g(x): x - a+ 2ae. Here a E R is a parameter. %3D (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

(1) Consider the Fixed Point iteration algorithm defined by the formula rn+1 = 9(xn), where g(r)
r - a + 2ae . Here a E R is a parameter.
%3D
(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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