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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.7: Applications
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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)
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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