ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS

A class of parallel nonlinear multisplitting AOR methods is set up by directly multisplitting the nonlinear mapping $ F: D\subset R^n\rightarrow R^n$ for solving the nonlinear system of equations $ F(x)=0$. The different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods as well as a lot of new relaxation parallel nonlinear multisplitting methods. The two-sided approximation properties and the influences on convergence from the relaxation parameters about the new methods are shown, and the sufficient conditions guaranteeing the methods to converge globally are discussed. Finally, a lot of numerical results show that the methods are feasible and efficient.