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 relaxa tion techniques, we present, in this paper, a class of parallel nonlin ear multisplitting successive overrelaxation methods for solving the l arge sparse nonlinear complementarity problems on the modern high-spee d multiprocessors. These new methods particularly include the so-calle d nonlinear multisplitting SOR Newton method, the nonlinear multisplit ting SOR-chord method, and the nonlinear multisplitting SOR-Steffensen method. Under suitable conditions, we establish the local convergence theories of the new methods, and investigate their asymptotic converg ence rates. A lot of numerical results show that our new methods are f easible and efficient for parallel solving the nonlinear complementari ty problems.