• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1489-1497
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• 2010

In this paper, we study convergence of both two-stage multisplitting method with preweighting and ILU-multisplitting method with preweighting for solving a linear system.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.727-741
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• 2010

In this paper, we study the convergence of relaxed two-stage multisplitting method using H-compatible splittings or SOR multisplitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an H-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.489-500
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• 2009

In this paper, we study the convergence of relaxed two-stage multisplitting method using M-splittings or SOR multi splitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an M-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.77-90
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• 2004

In this paper, we study the convergence of both relaxed multisplitting method and nonstationary two-stage multisplitting method associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is an H-matrix. Also, parallel performance results of nonstaionary two-stage multisplitting method using ILU factorizations as inner splittings on the IBM p690 supercomputer are provided to analyze theoretical results.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.25-35
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• 2009

In this paper, we study the regularity of induced splittings from multisplitting and two-stage multisplitting methods of monotone matrices under the assumption that splittings are weak regular, and we also study some comparison theorems for two-stage multisplitting methods of monotone matrices.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.501-510
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• 2008

In this paper, we first provide a convergence result of the generalized two-stage splitting method for solving a linear system whose coefficient matrix is an H-matrix, and then we provide convergence results of the generalized multisplitting and two-stage multisplitting methods for both a monotone matrix and an H-matrix.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.5.1-5
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• 2003

In this paper, we study the convergence of relaxed multisplitting and relaxed nonstationary two-stage multisplitting methods associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is an H-matrix. Also, parallel performance results of relaxed nonstaionary two-stage multisplitting method using ILU factorizations as inner splittings on the IBM p690 supercomputer are provided to analyze theoretical results.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.753-762
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• 2011

Recently, Cheng et al. [3] introduced new nonstationary multisplitting methods with multi-relaxed parameters. In this paper, we first provide correct proofs for convergence results of the multi-relaxed nonstationary multisplitting method which have not been proved completely by Cheng et al., and then we provide new convergence results for the multirelaxed nonstationary two-stage multisplitting method.