% Usage: [x n] = newton(f,df,x0,tol)
% Newton's method for solving f(x)=0
%
% Input:
% f - Matlab inline function f(x)
% df - Matlab inline function df(x), the derivative of f(x)
% x0 - initial guess
% tol - target tolerance: output x satisfies |f(x)| <= tol
%
% Output:
% x - computed solution
% n - number of iterations
%
% Examples:
% f=inline('sin(t)');
% df=inline('cos(t)');
% y=newton(f,df,1,0.01);

function [x n]= newton(f,df,x0,tol)
x = x0;
z = f(x);
n = 0;
while norm(z) > tol
    x = x - df(x) \ z;
    z = f(x);
    n = n + 1;
end;