function [P,p0,k,err,y] = newton2(f,df,p0,delta,epsilon,max1) 
%---------------------------------------------------------------------------
%NEWTON 2   Newton's method is used to locate a root.
% Sample calls
%   [P,p,k,err,y] = newton2(@f,df,p0,delta,epsilon,max1)
%   
% Inputs
%   f         name of the function
%   df        name of the function's derivative input
%   p0        starting value
%   delta     convergence tolerance for p0
%   epsilon   convergence tolerance for y0
%   max1      maximum number of iterations
% Return
%   p         solution: the root
%   y        solution: the function value
%   err       error estimate in the solution p0
% 
%If f and df are defined as M-file functions use the @ notation
% call [p0,err,k,y]=newton2(@f,@df,p0,delta,epsilon,max1).
%If f and df are defined as anonymous functions use the
% call  [p0,err,k,y]=newton2(f,df,p0,delta,epsilon,max1).



%---------------------------------------------------------------------------
P = [p0];
for k=1:max1
  p1 = p0 - feval(f,p0)/feval(df,p0);
  err = abs(p1-p0);
  P = [P p1];
  relerr = 2*err/(abs(p1)+delta);
  p0 = p1
  y = feval(f,p0)
  if (err<delta)|(relerr<delta)|(abs(y)<epsilon), break, end
end