Asynchronous Multisplitting GAOR Method and Asynchronous Multisplitting SSOR Method for Systems of Weakly Nonlinear Equations

In this article, we introduce two new asynchronous multisplitting methods for solving the system of weakly nonlinear equations Ax = G(x) in which A is an n × n real matrix and G(x) = (g1(x), g2(x), . . . , gn(x))T is a P-bounded mapping. First, by generalized accelerated overrelaxation (GAOR) technique, we introduce the asynchronous parallel multisplitting GAOR method (including the synchronous parallel multisplitting AOR method as a special case) for solving the system of weakly nonlinear equations. Second, asynchronous parallel multisplitting method based on symmetric successive overrelaxation (SSOR) multisplitting is introduced, which is called asynchronous parallel multisplitting SSOR method. Then under suitable conditions, we establish the convergence of the two introduced methods. The given results contain synchronous multisplitting iterations as a special case.