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Parallel performance of multisplitting methods with preweighting
한유두,윤재헌 대한수학회 2012 대한수학회지 Vol.49 No.4
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
한유두,Jae Heon Yun 대한수학회 2012 대한수학회보 Vol.49 No.5
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.
Convergence of SSOR multisplitting method for an M-matrix
윤재헌,한유두,오세영 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
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.
Modified incomplete Cholesky factorization preconditioners for a symmetric positive definite matrix
윤재헌,한유두 대한수학회 2002 대한수학회보 Vol.39 No.3
We propose variants of the modified incomplete Choleskyfactorization preconditioner for a symmetric positive definite(SPD) matrix. Spectral properties of these preconditioners arediscussed, and then numerical results of the preconditioned CG(PCG) method using these preconditioners are provided to see theeffectiveness of the preconditioners.
CONVERGENCE OF TWO-STAGE MULTISPLITTING AND ILU-MULTISPLITTING METHODS WITH PREWEIGHTING
윤재헌,한유두 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.5
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.
CONVERGENCE OF MULTISPLITTING METHODS WITH DIFFERENT WEIGHTING SCHEMES
오세영,윤재헌,한유두 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
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 the generalized multisplitting and two-stage multisplitting methods$^\dagger$
오세영,윤재헌,한유두 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
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.
Further results on multisplitting and two-stage multisplitting methods
Sang Wook Kim,윤재헌,한유두 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper, we study the regularity of induced splittings frommultisplitting and two-stage multisplitting methods of monotonematrices under the assumption that splittings are weak regular,and we also study some comparison theorems for two-stagemultisplitting methods of monotone matrices.