EFFICIENT TWO-STEPS ITERATIVE METHOD FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS

Abstract

In this paper, we present a new iterative method for solving nonlinear system of equations using Levenberg-Marquardt technique. The proposed method is a two-steps and proved to be globally convergent. The global convergence is achieved by incoperating the proposed algorithm with nonmonotone line search. The fourth-order of the scheme was obtained through computation of its computational order of convergence (COC). The strategy being a regularized method, solves most of the test functions that are singular in nature. Comparison for computation of efficiency index shows that the proposed method is robust in both classical or traditional efficiency index (TEI) and flops-like efficiency index (FEI). The convergence properties of the proposed method are also presented. In terms of less number of iterations and fast computing time, our proposed technique competes with other existing fourth-order methods nicely. Almost all the numerical performances conducted on some benchmark problems, have shown that the proposed algorithm is very efficient and promising.