A Concise Introduction to Programming in Python

Project: Newton’s Metho d

Newton’s method is a powerful technique for numerically computing the

zeros of differentiable functions. It is an iterative technique, meaning that

instead of applying a formula to directly compute the answer, it repeatedly

tries to compute a better approximation until the desired accuracy is reached.

Iteration is just a fancy word for repetition, which we know how to do in

Python using for loops and while loops.

Newton’s method gives a surprisingly simple algorithm for computing

√

k.

Listing 8.2: Newton’s Method (Algorithm)

# To compute sqrt(k)

Begin with an initial guess x.

Repeat until desired accuracy is reached:

Replace x with ...