Iterative method for solving nonlinear singular problems

Abstract

The aim of our work is to present a method ( p-factor method) for solving nonlinear equations of the formin singular (irregular) case, i.e. when the matrix F (x) is singular at an initial point x 0 of an iterative sequence {x k }, k = 1, 2, . . . We investigate conditions that have to be fulfilled at the initial point x 0 to obtain the existence of solution of nonlinear equation F(x) = 0, prove convergence of the presented p-factor method and give estimation of convergence rate for this method.