On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations

Abstract

A derivative-free quasi-Newton-type algorithm in which its search direction is a product of a positive definite diagonal matrix and a residual vector is presented. The algorithm is simple to implement and has the ability to solve large-scale nonlinear systems of equations with separable functions. The diagonal matrix is simply obtained in a quasi-Newton manner at each iteration. Under some suitable conditions, the global and R-linear convergence result of the algorithm are presented. Numerical test on some benchmark separable nonlinear equations problems reveal the robustness and efficiency of the algorithm.