newton.m

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function [p0,err,k,y]=newton(f,df,p0,delta,epsilon,max1)

%Input - f is the object function input as a string 'f'
%      - df is the derivative of f input as a string 'df'
%      - p0 is the initial approximation to a zero of f
%	    - delta is the tolerance for p0
%	    - epsilon is the tolerance for the function values y
%	    - max1 is the maximum number of iterations
%Output - p0 is the Newton-Raphson approximation to the zero
%	     - err is the error estimate for p0
%	     - k is the number of iterations
%	     - y is the function value f(p0)

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

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