Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

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

  • Oh, Se-Young (Department of Mathematics, Chungnam National University) ;
  • Yun, Jae-Heon (Department of Mathematics, College of Natural Sciences, Chungnam National University)
  • 발행 : 2009.05.31
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초록

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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참고문헌

  1. A. Berman and R.J. Plemmons, Nonnegative matrices in the Mathematical sciences, Academic Press, New York, 1979.
  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. D. Wang, On the convergence of the parallel multisplitting AOR algorithm, Linear Algebra Appl. 154-156 (1991), 473–486. https://doi.org/10.1016/0024-3795(91)90390-I
  4. 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
  5. M. Neumann and R.J. Plemmons, Convergence of parallel multisplitting methods for M-matrices, Linear Algebra Appl. 88-89 (1987), 559–574. https://doi.org/10.1016/0024-3795(87)90125-X
  6. SeYoung Oh, J.H. Yun and Y.D. Han, Convergence of the generalized multisplitting and two-stage multisplitting methods, J. Appl. Math. & Informatics. 26 (2008), 501–510.
  7. 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. https://doi.org/10.1137/0606062
  8. 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. https://doi.org/10.1137/0613042
  9. R.S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, 1962.
  10. D. Wang, On the convergence of the parallel multisplitting AOR algorithm, Linear Algebra Appl. 154-156 (1991), 473–486. https://doi.org/10.1016/0024-3795(91)90390-I
  11. 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