Convergence of nonstationary multisplitting methods using ILU factorizations

Authors:
Jae Heon Yun
Affiliations:
Department of Mathematics, College of Natural Sciences, Chungbuk National University, Cheongju, 48 Gaeshin-dong, Heungduk-Gu, Chungbuk 361-763, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 7
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Abstract

In this paper, we first study convergence of nonstationary multisplitting methods associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is a large sparse H-matrix. We next study a parallel implementation of the relaxed nonstationary two-stage multisplitting method (called Algorithm 2 in this paper) using ILU factorizations as inner splittings and an application of Algorithm 2 to parallel preconditioner of Krylov subspace methods. Lastly, we provide parallel performance results of both Algorithm 2 using ILU factorizations as inner splittings and the BiCGSTAB with a parallel preconditioner which is derived from Algorithm 2 on the IBM p690 supercomputer.