A quasi-newton like method via modified rational approximation model for solving system of nonlinear equation

Abstract

The major disadvantages of Newton method (NM) for nonlinear system of equations consist of finding and storing n × n Jacobin matrix which entail computation of the first derivatives in every iteration. In practice finding derivatives of some functions are often costly and sometime may not be available when the number of variables is large. In this paper, we proposed a new quasi newton like method via modified rational approximation model. Under certain condition, we show that this new algorithm has superlinear convergence rate. Numerical results have shown that the proposed method performed better than the classical methods for solving system of nonlinear equations.