Weighted Frobenius Norm Diagonal Quasi-Newton Method For Solving Large-Scale System of Nonlinear Equations

Abstract

One of the major shortcomings of the quasi-Newton methods and some of theirs variants in solving systems of nonlinear equations is computing and storing the approximation of the Jacobian matrix or its inverse at each iteration. This paper, presents a new method based on weighted Frobenius norm, with choice of the weighting matrix to be the identity matrix. The proposed method are matrix and derivative free. The basic idea is to incorporate Leong et al., [13] update via diagonal updating by least change secant update strategy. This can be achieved by using weighted Frobenius norm. The local convergence analysis of the scheme is presented. Numerical results carried out on some benchmark test problems show that the proposed method is promising compared to some existing conjugate gradient methods.