Newton's method roots on Matlab - matlab

Question

I am not so much experiences with Matlab. I just need it for the sake of solving some lengthy non-linear equations. Instead of using fzero, I wanna use Newton-Raphson's to solve the equation.
newton.m file contains the following code.
function [ x, ex ] = newton( f, df, x0, tol, nmax )
if nargin == 3
tol = 1e-4;
nmax = 1e1;
elseif nargin == 4
nmax = 1e1;
elseif nargin ~= 5
error('newton: invalid input parameters');
end
x(1) = x0 - (f(x0)/df(x0));
ex(1) = abs(x(1)-x0);
k = 2;
while (ex(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
And in the main file, I have called this function as follows:
ext_H = newton( exp(x) + x^3, diff(exp(x) + x^3), 9, 0.5*10^-5, 10);
When I run this function, it gives me the following error.
Error using sym/subsref (line 9)
Error using maplemex
Error, (in MTM:-subsref) Array index out of range
Error in newton (line 37)
x(1) = x0 - (f(x0)/df(x0));
Error in main (line 104)
ext_H = newton( exp(x) + x^3, diff(exp(x) + x^3), 9, 0.5*10^-5, 10);
Could anyone please help me to get through this?

Answer 1

You can probably use Matlab's fsolve (http://uk.mathworks.com/help/optim/ug/fsolve.html) with a couple of options
x0 = 9;
options = optimoptions('fsolve','Algorithm','levenberg-marquardt','TolFun',5*10^-6,'MaxIter',100);
x = fsolve(#(x)(exp(x) + x^3), x0,options);
or just fzero (http://uk.mathworks.com/help/optim/ug/fzero.html) which implements BD algorithm
x = fzero(#(x)(exp(x) + x^3), x0);