Consider the function f(x) = x² + 2x −5+ Inx. The function admits a single root located in the interval [1,2]. Consider the following method of fixed point Xn+1 = h(xn) with h(xn) = xn- yf(xn), (y>0) For which values of y, this method converges to the root.
Consider the function f(x) = x² + 2x −5+ Inx. The function admits a single root located in the interval [1,2]. Consider the following method of fixed point Xn+1 = h(xn) with h(xn) = xn- yf(xn), (y>0) For which values of y, this method converges to the root.
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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Consider the function f(x) = x^2 + 2x - 5 + lnx
The function admits a single root located in the interval [1,2].
Consider the following method of fixed point xn+1 = h(xn) with h(xn)= xn − yf(xn), (y > 0) .
For which values of y, this method converges to the root.
![Consider the function f(x) = x² + 2x −5+ Inx.
The function admits a single root located in the interval [1,2].
Consider the following method of fixed point xn+1 = h(xn) with h(xn) = xn- yf(xn), (y > 0).
For which values of y, this method converges to the root.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadae0aba-5d6a-460e-9444-9b07a6803c05%2F69c69eea-3cb3-4faa-ad42-a7edfe2d04aa%2Fg95t4wg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function f(x) = x² + 2x −5+ Inx.
The function admits a single root located in the interval [1,2].
Consider the following method of fixed point xn+1 = h(xn) with h(xn) = xn- yf(xn), (y > 0).
For which values of y, this method converges to the root.
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