Using approximate inverses in algebraic multilevel methods |
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Authors: | Y Notay |
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Institution: | (1) Service de Métrologie Nucléaire, Université Libre de Bruxelles (C.P. 165), 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium; e-mail: ynotay@ulb.ac.be , BE |
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Abstract: | Summary. This paper deals with the iterative solution of large sparse symmetric positive definite systems. We investigate preconditioning
techniques of the two-level type that are based on a block factorization of the system matrix. Whereas the basic scheme assumes
an exact inversion of the submatrix related to the first block of unknowns, we analyze the effect of using an approximate
inverse instead. We derive condition number estimates that are valid for any type of approximation of the Schur complement
and that do not assume the use of the hierarchical basis. They show that the two-level methods are stable when using approximate inverses
based on modified ILU techniques, or explicit inverses that meet some row-sum criterion. On the other hand, we bring to the
light that the use of standard approximate inverses based on convergent splittings can have a dramatic effect on the convergence
rate. These conclusions are numerically illustrated on some examples
Received March 3, 1997 / Revised version received July 16, 1997 |
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Keywords: | Mathematics Subject Classification (1991):65F10 65B99 65N20 |
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