1 +1 will converge to a 2pn-1 a) Show that the fixed point iteration of the forın Pn = unique fixed point in that interval for any initial guess po in the interval.
1 +1 will converge to a 2pn-1 a) Show that the fixed point iteration of the forın Pn = unique fixed point in that interval for any initial guess po in the interval.
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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Question
NUMERICAL ANALYSIS
Please solve part a
![Consider the equation 2x -
1
= 2 on the interval [1,2].
1.
1
+1 will converge to a
2pn-1
(a) Show that the fixed point iteration of the forn Pn =
unique fixed point in that interval for any initial guess po in the interval.
(b) Using an intial guess of po = 1.3, approxinate the solution of the equation to an
accuracy of 10-2 using the fixed point iteration given in part (a) and then again
using Newton's method. Determine which of the two sequences converges faster
and give the reason for that?
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a399ca2-ca03-4700-a442-b901b7bf1c54%2Fa8337406-38fb-4d95-863c-6a98737eb355%2Fff98ma_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the equation 2x -
1
= 2 on the interval [1,2].
1.
1
+1 will converge to a
2pn-1
(a) Show that the fixed point iteration of the forn Pn =
unique fixed point in that interval for any initial guess po in the interval.
(b) Using an intial guess of po = 1.3, approxinate the solution of the equation to an
accuracy of 10-2 using the fixed point iteration given in part (a) and then again
using Newton's method. Determine which of the two sequences converges faster
and give the reason for that?
%3D
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