A Reordering Strategy for Robust Incomplete A Reordering Strategy for Robust Incomplete
LU Factorizations of Indefinite Matrices1

Jing WANG
Department of Mathematics
Zhejiang University
China
Email: wroaring@sohu.com

A robust method of incomplete LU (ILU) factorization of an indefinite matrix A is proposed for preconditioned iterations. Our basic idea is to increase the row number of strictly diagonal dominance of A by diagonal scaling. We first reorder and partition the original matrix A as

PAPT = é
ê
ë
B
F
E
C
 ù
ú
û
(1)
according to the diagonal dominance, where [B, F] is strictly diagonally dominant. Then we determine a positive diagonal matrix D such that the matrix
~
A
 
 º é
ê
ë
B
F
E
C
 ù
ú
û 		é
ê
ë
D
I
 ù
ú
û
has more strictly dominant rows than A. This reordering strategy can be repeatedly applied to get
A1 º é
ê
ë
B1
F1
E1
C1
 ù
ú
û
that has approximately largest number of strictly dominant rows, where the block B1 is also strictly diagonally dominant and its size is larger than that of B. A partial ILU factorization is then applied to A1, which produces an approximate Schur complement matrix of C1. The whole process done on A is repeated on the small Schur complement matrix and continues for several times. This approach finally results to a multilevel ILU factorization of the original matrix A. Analyses are given to show that the process can not be broken and the Schur complement may have larger pivots. Numerical results are provided to compare the preconditioning strategy with other ILU preconditioning techniques.

Footnotes:

1 Work supported in part by the Special Funds for Major State Basic Research Projects of China (project G19990328) and Foundation for University Key Teacher by the Ministry of Education of China.

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On 15 Apr 2002, 12:34.