Matlab Code

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)

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

(c) John H. Mathews 2004