newtraph.m

% Newton-Raphson root finding - single function
%
% The function and its derivative are defined in another script
% file as follows: (Note that this won't accept vector inputs)
%
%   function [func, deriv] = fcn_nr(x)
%       func = x^4 - 5*x^3 - 124*x^2 + 380*x + 1200;
%       deriv = 4*x^3 - 15*x^2 - 248*x + 380;

% First, let's plot the function.
clear; clf; xp = -12:1:15; n = length(xp);
for i=1:n
  yp(i) = fcn_nr(xp(i));
end
quickplt(xp,yp,'x','f(x)','Plot of function','grid')
hold on

% now proceed with finding a root:

x = input('Enter initial guess of root location: ');

itermax = 100;      % max # of iterations
iter = 0;
errmax = 0.001;     % convergence tolerance
error = 1;
fprintf('\n   #      root       rel error\n\n');

while error > errmax & iter < itermax

  iter = iter + 1;
  [f fprime] = fcn_nr(x);
  if fprime == 0
    fprintf('ERROR: deriv(x) = 0; can''t divide by zero\n')
    break;
  end;

  xnew = x - f / fprime;    % here is new root estimate

  error = abs((xnew - x)/xnew) * 100;  % find change from previous
  fprintf('%3i   %10.6f   %10.5f\n',iter,xnew,error);
  x = xnew;      % set up for next iteration

end
plot(x, fcn_nr(x),'ro')