function [p0,err,P] = fixpt(g,p0,tol,max1)
%---------------------------------------------------------------------------
%FIXPT Fixed point iteration.
% Sample calls
% [p0,err] = fixpt('g',p0,tol,max1)
% [p0,err,P] = fixpt('g',p0,tol,max1)
% Return
% g name of the function
% p0 starting value
% tol convergence tolerance
% max1 maximum number of iterations
% Return
% p0 solution: the fixed point
% err error estimate in the solution
% P History vector of the iterations
%
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1995
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% Prentice Hall, Inc.; USA, Canada, Mexico ISBN 0-13-624990-6
% Prentice Hall, International Editions: ISBN 0-13-625047-5
% This free software is compliments of the author.
% E-mail address: in%"mathews@fullerton.edu"
%
% Algorithm 2.1 (Fixed Point Iteration).
% Section 2.1, Iteration for Solving x = g(x), Page 51
%---------------------------------------------------------------------------
P(1) = p0;
err = 1;
relerr = 1;
p1 = p0;
for k=1:max1,
p1 = feval(g,p0);
err = abs(p1-p0);
relerr = err/(abs(p1)+eps);
if (err<tol) | (relerr<tol), break; end
p0 = p1;
P(k+1) = p1;
end
