The Fixed-point iteration algorithm in Matlab

The Fixed-point iteration algorithm in Matlab :

function fixed_point(p0, N) %Fixed_Point(p0, N) approximates the root of the equation f(x) = 0 %rewritten in the form x = g(x), starting with an initial approximation p0. %The iterative technique is implemented N times. %The user has to enter the function g(x)at the bottom %Author: Alain G. Kapitho %Date : Jan. 2006 i = 1; p(1) = p0; tol = 1e-05; while i <= N p(i+1) = g(p(i)); if abs(p(i+1)-p(i)) < tol %stopping criterion disp('The procedure was successful after k iterations') k = i disp('The root to the equation is') p(i+1) return end i = i+1; end if abs(p(i)-p(i-1)) > tol | i > N disp('The procedure was unsuccessful') disp('Condition |p(i+1)-p(i)| < tol was not sastified') tol disp('Please, examine the sequence of iterates') p = p' disp('In case you observe convergence, then increase the maximum number of iterations') disp('In case of divergence, try another initial approximation p0 or rewrite g(x)') disp('in such a way that |g''(x)|< 1 near the root') end %this part has to be changed accordingly with the specific function g(x) function y = g(x) %y = x - x.^3 - 4*x.^2 + 10; %y = sqrt(10./x - 4*x); y = x - (x.^3 + 4*x.^2 - 10)/(3*x.^2 + 8*x);