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Incomplete block factorization methods for complex-structure matrices

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Abstract

Two classes of SSOR-type incomplete block factorization methods are proposed for preconditioning of linear algebraic systems of equations with block banded matrices of complex structure. Correctness conditions are derived for these methods in application to M-matrices and their efficiency is demonstrated by numerical experiments with linear algebraic systems obtained by discretization of the three-dimensional Poisson equation using quadratic and cubic serendipity finite elements.

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Literature cited

  1. A. Yu. Eremin and L. Yu. Kolotilina, On One Family of Two-Level Incomplete Block Factorization Preconditioners [in Russian], Preprint OVM AN SSSR No. 108, Moscow (1985).

  2. A. Yu. Eremin and L. Yu. Kolotina, On One Approach to the Construction of Incomplete Block Factorizations for Sparse Matrices of Complex Structure [in Russian], Preprint OVM AN SSSR No. 135, Moscow (1986).

  3. L. Yu. Kolotilina, On One Family of Explicit Preconditionings of Linear Algebraic Systems of Equations with Sparse Matrices [in Russian], Preprint LOMI R-8-86, Leningrad (1986).

  4. O. Axelsson, “Incomplete block matrix factorization preconditioning methods. The ultimate answer?,” J. Comput. Appl. Math.,12–13, 3–18 (1985).

    Article  MathSciNet  Google Scholar 

  5. O. Axelsson and B. Polman, “On approximate factorization methods for block matrices suitable for vector and parallel processors,” Linear Algebra Appl.,77, 3–26 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York (1979).

    MATH  Google Scholar 

  7. I. Efrat and M. Tismenetsky, “Parallel iterative linear solvers for oil reservoir models,” IBM J. Res. Develop.,30, No. 2, 184–192 (1986).

    Article  MathSciNet  Google Scholar 

  8. S. C. Eisenstat, H. C. Elman, and M. H. Schultz, “Block-preconditioned conjugate-gradientlike methods for numerical reservoir simulation,” Proc. SPE 1985 Reservoir Simulation Symp., Dallas, TX, 1985, Society of Petroleum Engineers of AIME (1985), pp. 397–405.

  9. Y. Saad, “Practical use of polynomial preconditionings for the conjugate gradient method,” SIAM J. Sci. Stat. Comput.,6, No. 4, 865–881 (1985).

    Article  MATH  MathSciNet  Google Scholar 

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Authors
  1. A. Yu. Eremin
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  2. L. Yu. Kolotilina
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 159, pp. 5–22, 1987.

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Eremin, A.Y., Kolotilina, L.Y. Incomplete block factorization methods for complex-structure matrices. J Math Sci 47, 2821–2834 (1989). https://doi.org/10.1007/BF01305210

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  • DOI: https://doi.org/10.1007/BF01305210

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