function [x_star,success] = newton (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
%
% [x_star,success] = newton(x0,f,f_prime,eps,maxitr)
% does iterations of Newton's method for a single variable,
% 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.
% For example, suppose an m-file xsqm2.m is available in Matlab's working
% directory, with the following contents:
% function [y] = xsqm2(x)
% y = x^2-2;
% return
% and an m-fine xsqm2_prime is also available, with the following
% function [y] = xsqm2_prime(x)
% y = 2*x;
% return
% contents:
% Then, issuing
% [x_star,success] = newton(1.5, 'xsqm2', 'xsqm2_prime', 1e-10, 20)
% from Matlab's command window will cause an approximation to the square
% root of 2 to be stored in x_star.
% 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.
success = 0;
x = x0;
for i=1:maxitr;
fval = feval(f,x);
if abs(fval) < eps;
success = 1;
disp(sprintf(' %10.0f %15.9f %15.9f ', i, x, fval));
x_star = x;
return;
end;
fpval = feval(f_prime,x);
if fpval == 0;
x_star = x0;
end;
disp(sprintf(' %10.0f %15.9f %15.9f ', i, x, fval));
x = x - fval / fpval;
end;
x_star =x0;