Find gradient numerically for the equation

I have the following equation:

where R is a 3x3 matrix and w is 3x1 vector, Hg is 3x3 matrix and hg is 3x1 vector.

In my algorithm, I need to find the gradient of the function numerically which is written in the following form:

As J(x) will return a scalar value, I guess gradient function can not be used. As I am new in this domain, can anyone help me to find a way to calculate the gradient numerically (whether any function name or psudocode or snippet)?

Thanks a lot in advance.

Answer 1

[Alan Weiss]

There are tools on the File Exchange that can help you find numerical approximations to derivatives. For example, see Adaptive Robust Numerical Differentiation by the impressive John D'Errico.

Alan Weiss

MATLAB mathematical toolbox documentation