Convergence of two-stage and multisplitting methods using various types of splittings

We first study the convergence of both two-stage iterative method and multisplitting methods using various types of splittings for solving a linear system whose coefficient matrix is an M-matrix or an H-matrix. We next study a parallel implementation of two-stage multisplitting method associated with a special multisplitting and an application of the two-stage multisplitting method to parallel preconditioner of Krylov subspace methods. Lastly, we provide parallel performance results of both two-stage multisplitting method and Krylov subspace method with a parallel preconditioner which is derived from two-stage multisplitting method on the IBM p690 supercomputer.