A class of parallel nonlinear multisplitting relaxation methods for the large sparse nonlinear complementarity problems

By making use of the nonlinear multisplitting and the nonlinear relaxation techniques, we present, in this paper, a class of parallel nonlinear multisplitting successive overrelaxation methods for solving the large sparse nonlinear complementarity problems on the modern high-speed multiprocessors. These new methods particularly include the so-called nonlinear multisplitting SOR-Newton method. Under suitable conditions, we establish the local convergence theories of the new methods, and investigate their asymptotic convergence rates. A lot of numerical results show that our new methods are feasible and efficient for parallel solving the nonlinear complementarity problems.