newtraph.m

function [root,ea,iter]=newtraph(func,dfunc,xr,es,maxit,varargin)
% newtraph: Newton-Raphson root location zeroes
% [root,ea,iter]=newtraph(func,dfunc,xr,es,maxit,p1,p2,...):
%   uses Newton-Raphson method to find the root of func
% input:
%   func = name of function
%   dfunc = name of derivative of function
%   xr = initial guess
%   es = desired relative error (default = 0.0001%)
%   maxit = maximum allowable iterations (default = 50)
%   p1,p2,... = additional parameters used by function
% output:
%   root = real root
%   ea = approximate relative error (%)
%   iter = number of iterations
if nargin<3,error('at least 3 input arguments required'),end
if nargin<4 || isempty(es),es=0.0001;end
if nargin<5 || isempty(maxit),maxit=50;end
iter = 0;
while (1)
  xrold = xr;
  xr = xr - func(xr)/dfunc(xr);
  iter = iter + 1;
  if xr ~= 0 
    ea = abs((xr - xrold)/xr) * 100;
  end
  if ea <= es || iter >= maxit, break, end
end
root = xr;