1 sin (r) f(x) = x² = x cos(x)+ 0, with xo 2 4 (1) Does Newton's method converge quadratically to the root r Ti E (0, 1]? If not, explain why? (2) Find the multiplicity of the root r = r1 of f(x). (3) Write out the Modified Newton's Method such that we have quadratical convergence.
1 sin (r) f(x) = x² = x cos(x)+ 0, with xo 2 4 (1) Does Newton's method converge quadratically to the root r Ti E (0, 1]? If not, explain why? (2) Find the multiplicity of the root r = r1 of f(x). (3) Write out the Modified Newton's Method such that we have quadratical convergence.
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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Solvef(x) =x2−xcos(x) +14−sin2(x)4= 0,withx0=π2.(1) Does Newton’s method converge quadratically to the rootr=r1∈[0,1]? If not, explain why?(2) Find the multiplicity of the rootr=r1off(x).(3) Write out the Modified Newton’s Method such that we havequadratical convergence.
![sin (x)
f(x) = x² – r cos(x) +
0, with ro
%3D
4
(1) Does Newton's method converge quadratically to the root r
TI E (0, 1]? If not, explain why?
(2) Find the multiplicity of the root r = r1 of f(x).
(3) Write out the Modified Newton's Method such that we have
quadratical convergence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96344119-693c-49c6-b06a-a46154ac473d%2F24324a38-0cdd-4c81-bcf0-1f5a0380c973%2Fqiihg5_processed.png&w=3840&q=75)
Transcribed Image Text:sin (x)
f(x) = x² – r cos(x) +
0, with ro
%3D
4
(1) Does Newton's method converge quadratically to the root r
TI E (0, 1]? If not, explain why?
(2) Find the multiplicity of the root r = r1 of f(x).
(3) Write out the Modified Newton's Method such that we have
quadratical convergence.
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