AN ASYNCHRONOUS PARALLEL NONLINEAR MULTISPLITING RELAXATION METHODS

Abstract

In this paper, we set up an asynchronous parallel nonlinear multisplitting relaxation methods for solving system of nonlinear equation. With special choices of the relaxed parameters in the new methods, not only can the convergence properties of them be improved, but also many applicable and efficient asynchronous parallel nonlinear multisplitting iteration methods; such as the Jacobi, Gauss-Seidel, SOR as well as the asynchronous parallel nonlinear multisplitting AOR-Newton, -Cord and Steffensen programs, etc., can be obtained Under proper conditions, we build convergence theories about these asynchronous methods, and estimate their asymptotic con- vergence rates in detailed manner.