Computational implementation of the multivariate Halley method for solving nonlinear systems of equations

Abstract

Cubicaliy convergent iterative methods for the solution of nonlinear systems of the multivariate Halley method, require first and second partial derivatives of the of the functions comprising the system. Automatic differentiation is used to automate the Halley method, HESSIAN and routines for the required operators and functions. A Pascal-SC which implements this method in a single-step iteration mode. The program nonlinear systems, and the results are compared with Newton's method.