Browse > Article
http://dx.doi.org/10.4134/BKMS.2012.49.5.997

CONVERGENCE OF MULTISPLITTING METHODS WITH PREWEIGHTING FOR AN H-MATRIX  

Han, Yu-Du (Department of Mathematics College of Natural Sciences Chungbuk National University)
Yun, Jae-Heon (Department of Mathematics College of Natural Sciences Chungbuk National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 997-1006 More about this Journal
Abstract
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.
Keywords
multisplitting method; preweighting; AOR multisplitting; SSOR multisplitting; H-matrix;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Z. H. Cao and Z. Y. Liu, Convergence of relaxed parallel multisplitting methods with different weighting schemes, Appl. Math. Comp. 106 (1999), no. 2-3, 181-196.   DOI   ScienceOn
2 A. Frommer and G. Mayer, Convergence of relaxed parallel multisplitting methods, Linear Algebra Appl. 119 (1989), 141-152.   DOI   ScienceOn
3 A. Frommer and G. Mayer, On the theory and practice of multisplitting methods in parallel computation, Computing 49 (1992), no. 1, 63-74.   DOI
4 M. Neumann and R. J. Plemmons, Convergence of parallel multisplitting iterative methods for M-matrices, Linear Algebra Appl. 88/89 (1987), 559-573.
5 D. P. O'Leary and R. E.White, Multisplittings of matrices and parallel solution of linear systems, SIAM J. Algebraic Discrete Methods 6 (1985), no. 4, 630-640.   DOI
6 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), no. 2, 671-679.   DOI
7 R. S. Varga, Matrix Iterative Analysis, Springer, Berlin, 2000.
8 C. L. Wang and J. H. Zhao, Further results on regular splittings and multisplittings, Int. J. Comput. Math. 82 (2005), no. 4, 421-431.   DOI   ScienceOn
9 R. E. White, Multisplitting with different weighting schemes, SIAM J. Matrix Anal. Appl. 10 (1989), no. 4, 481-493.   DOI
10 R. E. White, Multisplitting of a symmetric positive definite matrix, SIAM J. Matrix Anal. Appl. 11 (1990), no. 1, 69-82.   DOI
11 J. H. Yun, Performance of ILU factorization preconditioners based on multisplittings, Numer. Math. 95 (2003), 761-779.   DOI
12 A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.