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An incomplete LU ‐factorization algorithm based on block bordering
Author(s) -
Kolotilina L. Yu.,
Nikishin A. A.,
Yeremin A. Yu.
Publication year - 2000
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/1099-1506(200010/12)7:7/8<543::aid-nla212>3.0.co;2-v
Subject(s) - mathematics , block (permutation group theory) , algorithm , factorization , triangular matrix , algebraic number , incomplete lu factorization , sparse matrix , combinatorics , discrete mathematics , matrix decomposition , pure mathematics , invertible matrix , mathematical analysis , eigenvalues and eigenvectors , physics , quantum mechanics , gaussian
This paper suggests a new algorithm, called IBBLU, for constructing incomplete LU ‐factorizations of general non‐singular sparse matrices. This algorithm is based on the block bordering idea and uses factorized sparse approximate inverses to approximate the inverses of pivot blocks. The triangular factors L and U are represented in explicit‐implicit block form, which enhances the flop performance of the preconditioning. The algorithm suggested is theoretically justified for M ‐ and H ‐matrices, and its competitiveness with the best available algebraic preconditioning methods in both symmetric and unsymmetric cases is demonstrated numerically. Copyright © 2000 John Wiley & Sons, Ltd.