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CONVERGENCE OF MULTISPLITTING METHODS WITH PREWEIGHTING FOR AN H-MATRIX

한유두|Jae Heon Yun
대한수학회 (The Korean Mathematical Society)|2012.09|대한수학회보 (Bulletin of the KMS)|제49권 제5호|pp. 997-1006

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참고문헌

키워드

multisplitting methodpreweightingAOR multisplittingSSOR multisplittingH-matrix.
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초록

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.

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.

참고문헌 (12)

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  3. A. Frommer, "Convergence of relaxed parallel multisplitting methods", Lin- ear Algebra Appl, 119, pp.141~152 (1989)
  4. A. Frommer, "On the theory and practice of multisplitting methods in parallel computation", Computing, 49(1), pp.63~74 (1992)
  5. M. Neumann, "Convergence of parallel multisplitting iterative meth- ods for M-matrices", Linear Algebra Appl, 88, pp.559~573 (1987)
  6. D. P. O’Leary, "Multisplittings of matrices and parallel solution of linear systems", SIAM J. Algebraic Discrete Methods, 6(4), pp.630~640 (1985)
  7. D. B. Szyld, "Two-stage and multisplitting methods for the parallel solution of linear systems", SIAM J. Matrix Anal. Appl, 13(2), pp.671~679 (1992)
  8. R. S. Varga, "Matrix Iterative Analysis" (2000), Springer
  9. C. L. Wang, "Further results on regular splittings and multisplittings", Int. J. Comput. Math, 82(4), pp.421~431 (2005)
  10. R. E. White, "Multisplitting with different weighting schemes", SIAM J. Matrix Anal. Appl, 10(4), pp.481~493 (1989)
  11. R. E. White, "Multisplitting of a symmetric positive definite matrix", SIAM J. Matrix Anal. Appl, 11(2), pp.69~82 (1990)
  12. J. H. Yun, "Performance of ILU factorization preconditioners based on multisplittings", Numer. Math, 95, pp.761~779 (2003)

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