Abstract
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.
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