Determine, if any, all fixed points of f (x) = 2r? – 4. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(b) Determine, if any, all fixed points of f (x) = 2x? – 4.
(c) Given the function f (r) = r + 4r2 – 10, suppose that z =
of f (r).
i. Show that g (r) = V10 – r* is a form of f (r) which facilitates the fixed
point iteration.
%3D
%3D
1.5 is near to a root
ii. Apply the fixed point iteration to g (x) four times.
iii. Using the test for convergence, determine if the fixed point iteration near
the root will converge to the root.
Transcribed Image Text:(b) Determine, if any, all fixed points of f (x) = 2x? – 4. (c) Given the function f (r) = r + 4r2 – 10, suppose that z = of f (r). i. Show that g (r) = V10 – r* is a form of f (r) which facilitates the fixed point iteration. %3D %3D 1.5 is near to a root ii. Apply the fixed point iteration to g (x) four times. iii. Using the test for convergence, determine if the fixed point iteration near the root will converge to the root.
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