Parallel relaxed multisplitting methods for a symmetric positive definite matrix

We first study convergence of both the relaxed multisplitting method and the relaxed (nonstationary) two-stage multisplitting method using incomplete factorizations for solving a linear system whose coefficient matrix is a large sparse symmetric positive definite matrix. We next study a parallel implementation of the relaxed two-stage multisplitting method using incomplete factorizations as inner splittings and an application of the relaxed two-stage multisplitting method to parallel preconditioner of the CG (conjugate gradient) method. Lastly, we provide parallel performance results of both the relaxed two-stage multisplitting method and the CG method with a parallel preconditioner which is derived from the relaxed two-stage multisplitting method on the IBM p690 supercomputer.