Iteration methods with incomplete corrections and solution of nonlinear equations

Abstract

Basing on the theory of dynamic systems with inclomplete corrections [1-2], various methods of Gauss-Seidel-type for the numerical solution of nonlinear equations are formulated and analyzed. For special classes of equations some of these methods have already been discussed (e.g. [3-5]).\\ The results of the present paper provide statements on the asymptotic stability of equilibria for new classes of nonlinear systems.