A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination

Abstract

In this paperwe present an iterative method for the numerical solution of(1.1). The method is a variation ofNewton'smethod incorporating Gaussian elimination in such a way that the most recent information is always used at each step of the algorithm. After specifying the method in terms of an iteration function, we prove that the iteration converges locally and that the convergence is quadratic in nature. Computer results are given and a comparison is made with Newton's method; these results illustrate the effectiveness of the method for nonlinear systems containing linear or mildly nonlinear equations. 2. Notation. We shall introduce most of the notation as needed;however