Newton-Raphson Method

The Newton-Raphson method is a generalization of Newton's method for sets of equations. Suppose you want to find the simultaneous root of N equations of N variables

The Wronskian matrix is a matrix of the partial derivatives of each equation f_i with respect to x_j

With one equation and one variable, the solution was given by changing the value of x by f/f¢. With more than one equation, the solution is analogous.

Much like Newton's Method with one equation, with multiple equations there is an initial guess for the variables, and successive iterations to improve that guess.

The convergence process is carried out until either some convergence criterion (usually when two successive guesses are less than some percent difference) or until it is determined that the process is not likely to converge (i.e. no solution exists).