Assume that f : [0,2] → [0, 2] such that f and f' are continuous. Morcover, assume that max |f'(x)| = 0.517. IC(0,2] The fixed point iteration r, = f(n 1) with ro = 2 produced r1 = 1.6, r2 = 1.47, r3 = 1.225, and so on. With these limited information, at least how many iterations should be ran so that the resulting estimate is within 10 10 of the fixed point of f?
Assume that f : [0,2] → [0, 2] such that f and f' are continuous. Morcover, assume that max |f'(x)| = 0.517. IC(0,2] The fixed point iteration r, = f(n 1) with ro = 2 produced r1 = 1.6, r2 = 1.47, r3 = 1.225, and so on. With these limited information, at least how many iterations should be ran so that the resulting estimate is within 10 10 of the fixed point of f?
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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![Assume that f : [0,2] → [0, 2] such that f and f' are continuous. Morcover,
assume that
max |f'(x)| = 0.517.
IC(0,2]
The fixed point iteration r, = f(n 1) with ro = 2 produced #1
r3 = 1.225, and so on. With these limited information, at least how many iterations
should be ran so that the resulting estimate is within 10 10 of the fixed point of f?
1.6, r2 = 1.47,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc77e8ec7-465e-4f5f-a5c5-7c5a0eedd889%2Fb57faf25-edec-454e-ac7d-c0a0cd9bec72%2Fr5hsv6_processed.png&w=3840&q=75)
Transcribed Image Text:Assume that f : [0,2] → [0, 2] such that f and f' are continuous. Morcover,
assume that
max |f'(x)| = 0.517.
IC(0,2]
The fixed point iteration r, = f(n 1) with ro = 2 produced #1
r3 = 1.225, and so on. With these limited information, at least how many iterations
should be ran so that the resulting estimate is within 10 10 of the fixed point of f?
1.6, r2 = 1.47,
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