Abstract
This note fills a logical gap in the theory of incomplete block factorizations of the generalized SSOR type. Namely, it is shown that using the so-called factorized sparse approximate inverses it is possible to preserve the symmetry of a given Stieltjes or positive definite H-matrix A in its incomplete block factorization K and to insure simultaneously the convergence of the related splitting A=K−R. Bibliography: 3 titles.
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Literature Cited
A. Berman and R. J. Plemmons, “Nonnegative Matrices in the Mathematical Sciences,” Academic Press, New York (1979).
L. Kolotilina and B. Polman, “On incomplete block factorization methods of the generalized SSOR type forH-matrices,”Linear Algebra Appl.,177, 111–136 (1992).
L. Kolotilina and A. Yeremin, “Factorized sparse approximate inverse preconditionings I. Theory,” SIAMJ. Matrix Anal. Appl.,14, 45–58 (1993).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 219, 1994, pp. 42–52.
Translated by L. Yu. Kolotilina.
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Kolotilina, L.Y. Convergence of certain incomplete block factorization splittings. J Math Sci 86, 2828–2834 (1997). https://doi.org/10.1007/BF02356141
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DOI: https://doi.org/10.1007/BF02356141