Let f(x) = (x − 3)^5 and x0 is not equal to 3. For each n ≥ 0, determine xn+1 from xn by using Newton’s method for finding the root of the equation f(x) = 0. Show that the sequence {xn} converges to 3 linearly with rate 4/5.
Let f(x) = (x − 3)^5 and x0 is not equal to 3. For each n ≥ 0, determine xn+1 from xn by using Newton’s method for finding the root of the equation f(x) = 0. Show that the sequence {xn} converges to 3 linearly with rate 4/5.
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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Let f(x) = (x − 3)^5 and x0 is not equal to 3. For each n ≥ 0, determine xn+1 from xn by using Newton’s method for finding the root of the equation f(x) = 0. Show that the sequence {xn} converges to 3 linearly with rate 4/5.
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