• Journal of applied mathematics & informatics
• /
• v.30 no.3_4
• /
• pp.593-602
• /
• 2012

In this paper, we first introduce a special type of multisplitting method with different weighting scheme, and then we provide convergence results of multisplitting methods with different weighting schemes corresponding to both the AOR-like multisplitting and the SSOR-like multisplitting.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.997-1006
• /
• 2012

In this paper, we study convergence of multisplitting methods with preweighting for solving a linear system whose coefficient matrix is an H-matrix corresponding to both the AOR multisplitting and the SSOR multisplitting. Numerical results are also provided to confirm theoretical results for the convergence of multisplitting methods with preweighting.

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

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.25-35
• /
• 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
• /
• v.15 no.1_2
• /
• pp.77-90
• /
• 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
• /
• v.24 no.1_2
• /
• pp.273-282
• /
• 2007

In this paper, we study the convergence of both the multisplitting method and the relaxed multisplitting method associated with SOR or SSOR multisplittings for solving a linear system whose coefficient matrix is an M-matrix.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.5.1-5
• /
• 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
• /
• v.26 no.3_4
• /
• pp.501-510
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.727-741
• /
• 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
• /
• v.29 no.3_4
• /
• pp.753-762
• /
• 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.