fixed_point_method.m

   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   %
  19
  20   iterations = 0;
  21   prev = x0;
  22   current = g(x0);
  23
  24   while (norm(current - prev, Inf) > epsilon)
  25     prev = current;
  26     current = g(current);
  27     iterations = iterations + 1;
  28   end
  29
  30   fixed_point = current;
  31 end