4. (Fized-Point Iteration Method; Consider the problem of finding the root of the polynomial f(x) = x* - 0.89x - 1.08 in [1,2]. (i) Show that f(x) f(x) = 0 = x =1 - f'(x) on [1,2), thereby reducing the root-finding problem to the fixed-point problem for the function f(x) g(r) = 1 - f'(x) on [1, 2].
4. (Fized-Point Iteration Method; Consider the problem of finding the root of the polynomial f(x) = x* - 0.89x - 1.08 in [1,2]. (i) Show that f(x) f(x) = 0 = x =1 - f'(x) on [1,2), thereby reducing the root-finding problem to the fixed-point problem for the function f(x) g(r) = 1 - f'(x) on [1, 2].
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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Numerical Analysis & it’s applications.
Q4 part (i)
![4. (Fired-Point Iteration Method;
Consider the problem of finding the root of the polynomial
f(x) = x* – 0.89x – 1.08
in [1, 2].
(i) Show that
f(x)
f (x) = 0 = = x –
f'(x)
on [1,2], thereby reducing the root-finding problem to the fixed-point problem for the function
f(r)
g(x) = x -
f'(x)
on [1, 2].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc92fb0c-7643-4ce5-8ef2-0330ed27f016%2Fc0317975-1ec4-4654-806e-0d7192226487%2Fza7b3qi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. (Fired-Point Iteration Method;
Consider the problem of finding the root of the polynomial
f(x) = x* – 0.89x – 1.08
in [1, 2].
(i) Show that
f(x)
f (x) = 0 = = x –
f'(x)
on [1,2], thereby reducing the root-finding problem to the fixed-point problem for the function
f(r)
g(x) = x -
f'(x)
on [1, 2].
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