1 function [fixed_point, iterations] = fixed_point_method(g, epsilon, x0)

2 ## Find a fixed_point of the function `g` with initial guess x0.

3 ##

4 ## INPUTS:

5 ##

6 ## * ``g`` - The function to iterate.

7 ##

8 ## * ``epsilon`` - We stop when two successive iterations are within

9 ## epsilon of each other, taken under the infinity norm. halt the

10 ## search and return the current approximation.

11 ##

12 ## OUTPUTS:

13 ##

14 ## * ``fixed_point`` - The fixed point that we found.

15 ##

16 ## * ``iterations`` - The number of iterations that we performed

17 ## during the search.

18 ##

20 iterations = 0;

21 prev = x0;

22 current = g(x0);

24 while (norm(current - prev, Inf) > epsilon)

25 prev = current;

26 current = g(current);

27 iterations = iterations + 1;

28 end

30 fixed_point = current;

31 end