DOI QR코드

DOI QR Code

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)
  • Received : 2011.05.19
  • Published : 2012.09.30

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

References

  1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
  2. 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. https://doi.org/10.1016/S0096-3003(98)10120-0
  3. A. Frommer and G. Mayer, Convergence of relaxed parallel multisplitting methods, Linear Algebra Appl. 119 (1989), 141-152. https://doi.org/10.1016/0024-3795(89)90074-8
  4. A. Frommer and G. Mayer, On the theory and practice of multisplitting methods in parallel computation, Computing 49 (1992), no. 1, 63-74. https://doi.org/10.1007/BF02238650
  5. M. Neumann and R. J. Plemmons, Convergence of parallel multisplitting iterative methods for M-matrices, Linear Algebra Appl. 88/89 (1987), 559-573.
  6. 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. https://doi.org/10.1137/0606062
  7. 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. https://doi.org/10.1137/0613042
  8. R. S. Varga, Matrix Iterative Analysis, Springer, Berlin, 2000.
  9. C. L. Wang and J. H. Zhao, Further results on regular splittings and multisplittings, Int. J. Comput. Math. 82 (2005), no. 4, 421-431. https://doi.org/10.1080/00207160412331296607
  10. R. E. White, Multisplitting with different weighting schemes, SIAM J. Matrix Anal. Appl. 10 (1989), no. 4, 481-493. https://doi.org/10.1137/0610034
  11. R. E. White, Multisplitting of a symmetric positive definite matrix, SIAM J. Matrix Anal. Appl. 11 (1990), no. 1, 69-82. https://doi.org/10.1137/0611004
  12. J. H. Yun, Performance of ILU factorization preconditioners based on multisplittings, Numer. Math. 95 (2003), 761-779. https://doi.org/10.1007/s00211-003-0453-1