• Title, Summary, Keyword: multisplitting method

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CONVERGENCE OF MULTISPLITTING METHODS WITH DIFFERENT WEIGHTING SCHEMES

  • Oh, Se-Young;Yun, Jae-Heon;Han, Yu-Du
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.593-602
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    • 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.

CONVERGENCE OF RELAXED TWO-STAGE MULTISPLITTING METHOD USING AN OUTER SPLITTING

  • Yun, Jae-Heon
    • 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.

CONVERGENCE OF RELAXED TWO-STAGE MULTISPLITTING METHOD USING M-SPLITTINGS OR SOR MULTISPLITTING

  • Oh, Se-Young;Yun, Jae-Heon
    • 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.

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FURTHER RESULTS ON MULTISPLITTING AND TWO-STAGE MULTISPLITTING METHODS

  • Kim, Sang-Wook;Han, Yu-Du;Yun, Jae-Heon
    • 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.

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CONVERGENCE OF THE GENERALIZED MULTISPLITTING AND TWO-STAGE MULTISPLITTING METHODS

  • Oh, Se-Young;Yun, Jae-Heon;Han, Yu-Du
    • 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.

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CONVERGENCE OF MULTI-RELAXED NONSTATIONARY MULTISPLITTING METHODS

  • Oh, Se-Young;Yun, Jae-Heon
    • 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.

PARALLEL PERFORMANCE OF MULTISPLITTING METHODS WITH PREWEIGHTING

  • Han, Yu-Du;Yun, Jae-Heon
    • Journal of the Korean Mathematical Society
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    • v.49 no.4
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    • pp.805-827
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    • 2012
  • In this paper, we first study convergence of a special type of multisplitting methods with preweighting, and then we provide some comparison results of those multisplitting methods. Next, we propose both parallel implementation of an SOR-like multisplitting method with preweighting and an application of the SOR-like multisplitting method with preweighting to a parallel preconditioner of Krylov subspace method. Lastly, we provide parallel performance results of both the SOR-like multisplitting method with preweighting and Krylov subspace method with the parallel preconditioner to evaluate parallel efficiency of the proposed methods.

CONVERGENCE OF MULTISPLITTING METHODS WITH PREWEIGHTING FOR AN H-MATRIX

  • Han, Yu-Du;Yun, Jae-Heon
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.997-1006
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    • 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.

Relaxed multisplitting and relaxed nonstationary two-stage multisplitting methods

  • 윤재헌
    • Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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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.

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