oneptrx.m

% Demonstration of One Point Iteration WITH RELAXATION
clear;

% define the function and its x = g(x) version
f = 'x^4 - 5*x^3 - 124*x^2 + 380*x + 1200';
% version 1 of g(x)
disp('Version 1 of g')
g = '-1200/(x^3 - 5*x^2 - 124*x + 380)';
% version 2 of g(x)
%disp('Version 2 of g')
%g = '(5*x^3 + 124*x^2 - 380*x - 1200)/x^3';
% version 3 of g(x)
%disp('Version 3 of g')
%g = '(-x^4 + 5*x^3 - 380*x - 1200)/(-124*x)';


       x = input ('Enter initial guess of root : ');
       W = input ('Enter relaxation factor W   : ');
maxerror = 0.1; % maximum error
   maxit = 30;  % maximum number of iterations
   count = 0;   % iteration counter
   error = 1;   % starting error (100 percent)

fprintf('\n Iteration      x       g(x)     error(%%)    f(x)\n\n');

% this is where all the work gets done.....

while (error > maxerror) & (count < maxit)
  count = count + 1;
  temp = eval(g);

  xnew = x + W*(temp - x);

  error = abs((xnew - x)/xnew) * 100;
  fprintf('%7g %10.4f %10.4f %10.4f  %10.4f\n',count,x,xnew,error,eval(f));
  x = xnew;
end

fprintf('\nRoot is %g   Function at root is %g\n',x,eval(f))