Numerical Computing :: Project Three

The goal of this project is to study what “local” means for convergence of Newton’s method. Consider the function

f(x) =
1

−
1
,x ∈ [−5, 5].
(1)











1 + exp(x)

2



The true root of this function is r = 0. You want to find an interval [a, b] satisfying two criteria:

    1. the length b − a is as large as possible

    2. 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