Description
The goal of this project is to study what “local” means for convergence of
Newton’s method. Consider the function
f(x) = 1
1 + exp(x)
−
1
2
, x ∈ [−5, 5]. (1)
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
