Newton Raphsons method in Matlab?

Question

Newtons-Raphsons method is easy to implement in Mathematica but in Matlab it seems a bit difficult. I don't get if I can pass a function to a function and how to use the derivative as a function.

newtonRaphson[f_, n_, guess_] := 
 If[n == 0, guess, newtonRaphson[f, n - 1, guess - f[guess]/f'[guess]]]
newtonRaphsonOptimize[f_, n_, guess_] := 
 If[n == 0, guess, 
  newtonRaphsonOptimize[f, n - 1, guess - f'[guess]/f''[guess]]]

It doesn't seem like you can derive neither function-handles nor functions defined in a file but I might be wrong.

Answer 1

You could use an implementation like this:

function x = newton(f,dfdx,x0,tolerance)
err = Inf;
x = x0;
while abs(err) > tolerance
   xPrev = x;
   x = xPrev - f(xPrev)./dfdx(xPrev);
   % stop criterion: (f(x) - 0) < tolerance
   err = f(x); % 
   % stop criterion: change of x < tolerance
   % err = x - xPrev;
end

And pass it function handles of both the function and its derivative. This derivative is possible to acquire by some different methods: manual differentiation, symbolic differentiation or automatic differentiation. You can also perform the differentiation numerically, but this is both slow and requires you to use a modified implementation. So I will assume you have calculated the derivative in any suitable way. Then you can call the code:

f = @(x)((x-4).^2-4);
dfdx = @(x)(2.*(x-4));
x0 = 1;
xRoot = newton(@f,@dfdx,x0,1e-10);