Consider the equation 2x - 1 = 2 on the interval [1, 2]. 1 +1 will converge to a 2pn-1 Show that the fixed point iteration of the form pn = unique fixed point in that interval for any initial guess po in the interval. Using an intial guess of po = 1.3, approxiinate the solution of the equation to an accuracy of 10-2 using the fixed point iteration given in part (a) and then again Lising Newton's method. Determine which of the two sequences converges faster and give the reason for that?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Part b
Consider the equation 2x
1
= 2 on the interval [1, 2].
|
(a) Show that the fixed point iteration of the form pn =
1
+1 will converge to a
2pn-1
unique fixed point in that interval for any initial guess po in the interval.
(b) Using an intial guess of po =
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?
1.3, approxiinate the solution of the equation to an
Transcribed Image Text:Consider the equation 2x 1 = 2 on the interval [1, 2]. | (a) Show that the fixed point iteration of the form pn = 1 +1 will converge to a 2pn-1 unique fixed point in that interval for any initial guess po in the interval. (b) Using an intial guess of po = 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? 1.3, approxiinate the solution of the equation to an
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