Newton Raphson Optimization Procedure

Newton Raphson Optimization Procedure for a set of Non-Linear Equations

It estimates the Newton Raphson optimization procedure for (m) unknowns of (n) non-linear equations. In case no Jacobian vector is presented, then the initial Jacobian vector is estimated by Broyden Method (multivariate secant approach) and it is then updated using the Sherman Morrison formula.

Usage:
[x, results] = newtonraphson(@f, @df, startingvals, TolX, MaxIter);
f is the M-file containing the functions, while df is the M-file containing the Jacobian vector. In case the tolerance (TolX) or the maximum number of iterations are not specified then the default values are set to: 1e-8 and 500, respectively.

The g.m is an example function with two unknows and two equations, and dg.m the Jacobian vector of the example function. Finally, the same solution will be reached either by specifying the Jacobian or not. (for instance: newtonraphson(@g, @dg, [-10; -10] ,[], []) or newtonraphson(@g, [], [-10; -10] ,[], []) ) although a larger number of iterations is required.