A necessary and sufficient condition for M-matrices and its relation to block LU factorization
We present a necessary and sufficient condition for M-matrices in terms of a special diagonal dominance. Then we use the new result to show that if the block comparison matrix of a block matrix A ̄ is an M-matrix, there exists a block permutation matrix P such that block LU factorization applied to...
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| Published in | Linear algebra and its applications Vol. 235; pp. 261 - 274 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.03.1996
|
| Online Access | Get full text |
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| Summary: | We present a necessary and sufficient condition for
M-matrices in terms of a special diagonal dominance. Then we use the new result to show that if the block comparison matrix of a block matrix
A
̄
is an
M-matrix, there exists a block permutation matrix
P such that block
LU factorization applied to
A = P
T
A
̄
P
is stable—i.e., the norms of the block multipliers −
A
(
k − 1)
i,
k
A
(
k − 1)
k,
k
are bounded by 1. We also present a collection of tools in the literature related to the subject matter. We define incomplete
M-matrices, prove a necessary and sufficient condition for such matrices, and present their implications for block
LU factorization. |
|---|---|
| ISSN: | 0024-3795 1873-1856 |
| DOI: | 10.1016/0024-3795(94)00164-2 |