Conditioning analysis of block incomplete factorizations and its application to elliptic equations |
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Authors: | Hao Lu Owe Axelsson |
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Institution: | (1) Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands , NL;(2) Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands , NL |
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Abstract: | Summary. The paper deals with eigenvalue estimates for block incomplete factorization methods for symmetric matrices. First, some
previous results on upper bounds for the maximum eigenvalue of preconditioned matrices are generalized to each eigenvalue.
Second, upper bounds for the maximum eigenvalue of the preconditioned matrix are further estimated, which presents a substantial
improvement of earlier results. Finally, the results are used to estimate bounds for every eigenvalue of the preconditioned
matrices, in particular, for the maximum eigenvalue, when a modified block incomplete factorization is used to solve an elliptic
equation with variable coefficients in two dimensions. The analysis yields a new upper bound of type for the condition number of the preconditioned matrix and shows clearly how the coefficients of the differential equation
influence the positive constant .
Received March 27, 1996 / Revised version received December 27, 1996 |
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Keywords: | Mathematics Subject Classification (1991): 65F10 65F15 65F50 |
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