Consider the following fixed-point iteration algorithm ,41 From a graphical solution of z = g(z) you know that z = 2.24 is approximately the fixed point of z g(z). If you start the fixed-point algorithm with z. = 2.38, how many iterations you need to perform at least in order to reach an error less than 10? Use your knowledge about the order of convergence of the fixed-point method to conduct your analysis. Answer

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Consider the following fixed-point iteration algorithm
1 = 9(z,)
From a graphical solution of z = g(z) you know that z = 2.24 is approximately the fixed point of I = g(z).
If you start the fixed-point algorithm with z, = 2.38, how many iterations you need to perform at least in order to reach an error less
than 10?
Use your knowledge about the order of convergence of the fixed-point method to conduct your analysis.
!!
Answer
Transcribed Image Text:Consider the following fixed-point iteration algorithm 1 = 9(z,) From a graphical solution of z = g(z) you know that z = 2.24 is approximately the fixed point of I = g(z). If you start the fixed-point algorithm with z, = 2.38, how many iterations you need to perform at least in order to reach an error less than 10? Use your knowledge about the order of convergence of the fixed-point method to conduct your analysis. !! Answer
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