A ABS algorithm for solving singular nonlinear system with space transformation

Abstract

A modified ABS algorithm for solving a class of singular nonlinear systems, F (x) = 0, where x, F ∈ R n , is presented. This method is constructed by combining the discreted Brown algorithm with the space transformation method. The second order information of F (x) at a point is not required calculating, which is different from the tensor method and the Hoy's method. The Q-quadratic convergence of this algorithm and some numerical examples are given as well.