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Mathematics of Computation

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A framework for block ILU factorizations using block-size reduction

Authors: Tony F. Chan and Panayot S. Vassilevski
Journal: Math. Comp. 64 (1995), 129-156
MSC: Primary 65F30
MathSciNet review: 1257575
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Abstract: We propose a block ILU factorization technique for block tridiagonal matrices that need not necessarily be M-matrices. The technique explores reduction by a coarse-vector restriction of the block size of the approximate Schur complements computed throughout the factorization process. Then on the basis of the Sherman-Morrison-Woodbury formula these are easily inverted. We prove the existence of the proposed factorization techniques in the case of (nonsymmetric, in general) M-matrices. For block tridiagonal matrices with positive definite symmetric part we show the existence of a limit version of the factorization (exact inverses of the reduced matrices are needed). The theory is illustrated with numerical tests.

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Keywords: Block ILU factorization, M-matrices, positive definite matrices, second-order elliptic equation, finite differences, Sherman-Morrison-Woodbury formula
Article copyright: © Copyright 1995 American Mathematical Society

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