Develop a program using a programming or macro language to i

Develop a program using a programming or macro language to implement Newton\'s method. The subroutine should have the following features: Iterate until the relative error falls below a stopping criterion or exceeds a maximum number of iterations. Returns both the optimal x and f(x).

Solution

function [ x, ex ] = newton( f, df, x0, tol, nmax )
%
% NEWTON Newton\'s Method
% Newton\'s method for finding successively better approximations to the
% zeroes of a real-valued function.
%
% Input:
% f - input funtion
% df - derived input function
% x0 - inicial aproximation
% tol - tolerance
% nmax - maximum number of iterations
%
% Output:
% x - aproximation to root
% ex - error estimate
% f -function
% Example:
%   [ x, f ] = newton( \'exp(x)+x\', \'exp(x)+1\', 0, 0.5*10^-5, 10 )
%

if nargin == 3
tol = 1e-4;
nmax = 1e1;
elseif nargin == 4
nmax = 1e1;
elseif nargin ~= 5
error(\'newton: invalid input parameters\');
end
  
f = inline(f);
df = inline(df);
x(1) = x0 - (f(x0)/df(x0));
ex(1) = abs(x(1)-x0);
k = 2;
while (ex(k-1)/abs(x(k-1)) >= tol) && (k <= nmax)
x(k) = x(k-1) - (f(x(k-1))/df(x(k-1)));
ex(k) = abs(x(k)-x(k-1));
k = k+1;
end

end