The Numerical Solution of Systems of Nonlinear Equations by an Extension of Hirano's Method and Armijo's Rule

Abstract

Abstract. This paper presents a new numerical algorithm for solving systems of nonlinear equations. The objective is to nd a solution near the initial approximate solution. In order to realize this, we apply an idea similar to Hirano's method for algebraic equations and Armijo's rule for nonlinear optimization. The effectiveness of the proposed method is demonstrated by numerical experiments on various systems of algebraic and nonlinear equations.