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http://dx.doi.org/10.14317/jami.2011.29.3_4.753

CONVERGENCE OF MULTI-RELAXED NONSTATIONARY MULTISPLITTING METHODS  

Oh, Se-Young (Department of Mathematics, Chungnam National University)
Yun, Jae-Heon (Department of Mathematics, College of Natural Sciences, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 753-762 More about this Journal
Abstract
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.
Keywords
nonstationary multisplitting method; ILU factorization; H-matrix; multisplitting;
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1 R. Bru, and R. Fuster, Parallel chaotic extrapolated Jacobi method. Appl. Math. Lett. 3 (1990), 65-69.
2 R. Bru, V. Migallon, J. Penades and D.B. Szyld, Parallel, synchronous and asynchronous two-stage multisplitting methods. Electron. Trans. Numer. Anal. 3 (1995), 24-38.
3 G.H Cheng, T.Z. Huang, Y.F Jing and L.T Zhang, Convergence behaviors of multisplitting methods with K+1 relaxed parameters, J. Comput. Appl. Math. 229 (2009), 61-69.   DOI   ScienceOn
4 A. Frommer and G. Mayer, Convergence of relaxed parallel multisplitting methods. Linear Algebra Appl. 119 (1989), 141-152.
5 A. Frommer and D.B. Szyld, H-splittings and two-stage iterative methods. Numer. Math. 63 (1992), 345-356.   DOI   ScienceOn
6 Y.D. Han and J.H. Yun, Convergence of two-stage multisplitting and ILU-multisplitting methods with preweighting. J. Appl. Math. & Informatics 28 (2010), 1489-1197.
7 S.W. Kim and J.H. Yun, Block ILU factorization preconditioners for a block-tridiagonal H-matrix. Linear Algebra Appl. 317 (2000), 103-125.   DOI
8 S. Oh and J.H. Yun, Convergence of relaxed two-stage multisplitting method using M- splittings or SOR multisplitting. J. Appl. Math. & Informatics 27 (2009), 489-500.
9 A. Messaoudi, On the stability of the incomplete LU factorizations and characterizations of H-matrices. Numer. Math. 69 (1995), 321-331.   DOI   ScienceOn
10 M. Neumann and R.J. Plemmons, Convergence of parallel multisplitting methods for M- matrices. Linear Algebra Appl. 88-89 (1987), 559-574.
11 D.P. O'Leary and R.E. White, Multisplittings of matrices and parallel solution of linear systems. SIAM J. Algebraic Discrete Meth. 6 (1985), 630-640.   DOI
12 D.B. Szyld and M.T. Jones, Two-stage and multisplitting methods for the parallel solution of linear systems. SIAM J. Matrix Anal. Appl. 13 (1992), 671-679.   DOI
13 R.E. White, Multisplitting of a symmetric positive de?nite matrix. SIAM J. Matrix Anal. Appl. 11 (1990), 69-82.   DOI
14 J.H. Yun, Performance of ILU factorization preconditioners based on multisplittings, Numer. Math. 95 (2003), 761-779.   DOI   ScienceOn