Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Problem 4 For each of the functions given below, use the Newton's method algorithm to approximate all real roots. Use an absolute tolerance of 10-6 as a stopping condition. For each of the roots plot the logarithm of the absolute error len] at each iteration n against the logarithm of the absolute error at the previous iteration. Use this plot to calculate the order of convergence. a) f(x) = ex+x2-x-7 b) f(x)=x²-x²-9x+4 c) f(x) = 1.08 - 1.03x + In (x)
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Transcribed Image Text:Problem 4 For each of the functions given below, use the Newton's method algorithm to approximate all real roots. Use an absolute tolerance of 10-6 as a stopping condition. For each of the roots plot the logarithm of the absolute error len] at each iteration n against the logarithm of the absolute error at the previous iteration. Use this plot to calculate the order of convergence. a) f(x) = ex+x2-x-7 b) f(x)=x²-x²-9x+4 c) f(x) = 1.08 - 1.03x + In (x)
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Step 1: Introduction
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Step 2: Newton's method algorithm
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Step 3: Iteration 2
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Step 4: Iteration 4
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