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1. Let f(z) = r -4 and g(r) = +. You can take as given that for r= 4/3, f(r) = 0 and g(r) =r. %3D %3D %3D (a) As Newton's method converges to the root r of f, estimate e+1 in terms of e̟. (b) As fired point itoratio

1. Let f(z) = r -4 and g(r) = +. You can take as given that for r= 4/3, f(r) = 0 and g(r) =r. %3D %3D %3D (a) As Newton's method converges to the root r of f, estimate e+1 in terms of e̟. (b) As fired point itoratio

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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1. Let f(r) = r – 4 and g(r) = 4 +. You can take as given that for r = 4/3, f(r) = 0 and g(r) =r. %3D %3D (a) As Newton's method converges to the root r of f, estimate ei+1 in terms of e. (b) As fixed point iteration converges to the fixed point r of g, estimate e+1 in terms of e. (c) Considering these three methods for finding 4/3, rank them from slowest to fastest: (i) bisection method applied to f: (ii) Newton's method applied to f; (iii) fixed point iteration applied to g.
Transcribed Image Text:1. Let f(r) = r – 4 and g(r) = 4 +. You can take as given that for r = 4/3, f(r) = 0 and g(r) =r. %3D %3D (a) As Newton's method converges to the root r of f, estimate ei+1 in terms of e. (b) As fixed point iteration converges to the fixed point r of g, estimate e+1 in terms of e. (c) Considering these three methods for finding 4/3, rank them from slowest to fastest: (i) bisection method applied to f: (ii) Newton's method applied to f; (iii) fixed point iteration applied to g.
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