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Existence and Conditioning Properties of Sparse Approximate Block Factorizations

Robert Beauwens and Mustapha Ben Bouzid
SIAM Journal on Numerical Analysis
Vol. 25, No. 4 (Aug., 1988), pp. 941-956
Stable URL: http://www.jstor.org/stable/2157612
Page Count: 16
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Existence and Conditioning Properties of Sparse Approximate Block Factorizations
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Abstract

A particular class of sparse approximate block LU factorizations is investigated. Sufficient conditions are determined for the existence of B = LP-1 U for a given coefficient matrix A. Bounds on the spectral condition number of B-1 A are obtained for symmetric B and A. When applied to discrete multidimensional elliptic partial differential equations, these results lead, under reasonable assumptions, to O(h-1) spectral condition numbers.

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