On Newton-GHSS Method For Systems Of Nonlinear Equations With Positive Definite Jacobian Materices

This paper considers the use of inexact Newton method for solution ofnonlinear equations with positive definite Jacobian matrices. Method ofinexact Newton in essence is a kind of inner and outer iterations, outeriteration for the classic method, GHSS iteration which can be used in theinner iterative algorithms of linear iterative method.GHSS method is an unconditionally convergent iteration method forsolving non-Hermitian positive definite system of linear equations, as theinexact Newton method within the iterative solver. We establish a class ofNewton-GHSS methods for solving systems of nonlinear equations withpositive definite Jacobian matrices at the solution points. And the local andsemi-local convergence of the method is analyzed in detail, when the initialvalue is given when certain conditions are satisfied and the method is semilocal convergence. The numerical results verify the feasibility andeffectiveness of this method.