The generalised Newton-Raphson method is an iterative algorithm for solving a set of simultaneous equations in an equal number of unknowns. At each iteration of the N-R method, the nonlinear problem is approximated by the linear-matrix equation. The linearising approximation can best be visualised in the case of a single-variable problem. The Newton-Raphson algorithm will converge quadratically if the functions have continuous first derivatives in the neighbourhood of the solution, the Jacobian matrix is nonsingular and the initial approximations of x are close to the actual solutions. However, the method is sensitive to the behaviours of the functions fk(xm) and, hence, to their formulation; the more linear they are, the more rapidly and reliably Newton's method converges. Nonsmoothness, i.e. humps, in any one of the functions in the region of interest, can cause convergence delays, total failure or misdirection to a nonuseful solution.