(a) Verify that √a is a fixed point of the function 1 a g(x) 9) =j (+4). x 2 (b) Assume that, for some po, the fixed point iteration Pn+1 converges to p = √a as n → ∞. Determine the order of convergence. = g(Pn)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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(a) Verify that √a is a fixed point of the function
g(x) = 1/2 (x + ²)
a).
(b) Assume that, for some po, the fixed point iteration Pn+1
converges to p = √a as n →∞. Determine the order of convergence.
=
g(Pn)
Transcribed Image Text:(a) Verify that √a is a fixed point of the function g(x) = 1/2 (x + ²) a). (b) Assume that, for some po, the fixed point iteration Pn+1 converges to p = √a as n →∞. Determine the order of convergence. = g(Pn)
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