List of nonlinear solvers

Iterative method

Algorithm 3 (Iterative method)

Inputs A function \(f\) and an initial guess \(x_0\)

Output An approximation \(x\) to a root of \(f\)

1. Set \(x_0\)

2. For \(n = 0, 1, 2, \ldots\) do

   1. Set \(x_{n+1} = f(x_n)\)

Newton’s method

Algorithm 4 (Newton’s method)

Inputs A function \(f\) and an initial guess \(x_0\)

Output An approximation \(x\) to a root of \(f\)

1. Set \(x_0\)

2. For \(n = 0, 1, 2, \ldots\) do

   1. Set \(x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}\)