Programming a Recursive Function

Hi

I know in the meantime how to program simple recursive functions, but wondered how Newton's method could be programmed recursively.

Especially, I would like to store for n iterations the resulting values in an vector of length n.

So I would have (as a sketch) something as follows in mind:

function v = newton(n)

% the function
f(n) = x^2;
% the derivative of f
g(n) = 2*x;
x_0 = 1;

for n > 1

v(n) = newton(n-1) - f(newton(n))/g(newton(n))

for n == 1

newton(n) = x_0

end

Could you please help me to correct the code?

Thanks for your efforts