Description
The goal of this project is to study what “local” means for convergence of Newton’s method. Consider the function
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f(x) =
1
−
1
,x ∈ [−5, 5].
(1)
1 + exp(x)
2
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The true root of this function is r = 0. You want to find an interval [a, b] satisfying two criteria:
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the length b − a is as large as possible
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Newton’s method converges for any initial guess in the interval, x0 ∈ [a, b].
You’ll determine the interval endpoints a and b using a computer experiment. Describe the rationale behind your choice of experiment, and report the results.
1
