function [x_star,success] = newton_sys (x0 ,f , f_prime, eps, maxitr)
% Accompanying program for the text
%
% Classical and Modern Numerical Analysis:
% Theory, Methods and Practice
% by Azmy S. Ackleh, Edward J. Allen,
% R. Baker Kearfott, and Padmanabhan Seshaiyer
%
% (Taylor and Francis / CRC Press, 2009)
%
% [x_star,success] = newton_sys(x0,f,f_prime,eps,maxitr)
% does iterations of Newton's method for systems,
% using x0 as initial guess, f (a character string giving
% an m-file name) as function, and f_prime (also a character
% string giving an m-file name) as the derivative of f.
% iteration stops successfully if ||f(x)|| < eps, and iteration
% stops unsuccessfully if maxitr iterations have been done
% without stopping successfully or if a zero derivative
% is encountered.
% On return:
% success = 1 if iteration stopped successfully, and
% success = 0 if iteration stopped unsuccessfully.
% x_star is set to the approximate solution to f(x) = 0
% if iteration stopped successfully, and x_star
% is set to x0 otherwise.
% This program was produced from minor modification of newton.m.
success = 0;
x = x0;
for i=1:maxitr;
fval = feval(f,x);
i
x
norm_fval = norm(fval,2)
if norm_fval < eps;
success = 1;
x_star = x;
return;
end;
fpval = feval(f_prime,x);
if fpval == 0;
x_star = x0;
end;
v = fpval \(-fval);
x = x +v;
end;
x_star =x0;
if (~success)
disp('Warning: Maximum number of iterations reached');
end