.png){kind=icon}
Return
A column approximate minimum degree ordering algorithm
.png){kind=icon}
PRE
AI
DOI：10.1145/1024074.1024079.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Sparse Gaussian elimination with partial pivoting computes the factorization
PAQ
=
LU
of a sparse matrix
A
, where the row ordering
P
is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering,
Q
, based solely on the nonzero pattern of
A
, that limits the worst-case number of nonzeros in the factorization. The fill-in also depends on
P
, but
Q
is selected to reduce an upper bound on the fill-in for any subsequent choice of
P
. The choice of
Q
can have a dramatic impact on the number of nonzeros in
L
and
U
. One scheme for determining a good column ordering for
A
is to compute a symmetric ordering that reduces fill-in in the Cholesky factorization of
A
T
A
. A conventional minimum degree ordering algorithm would require the sparsity structure of
A
T
A
to be computed, which can be expensive both in terms of space and time since
A
T
A
may be much denser than
A
. An alternative is to compute
Q
directly from the sparsity structure of
A
; this strategy is used by MATLAB's COLMMD preordering algorithm. A new ordering algorithm, COLAMD, is presented. It is based on the same strategy but uses a better ordering heuristic. COLAMD is faster and computes better orderings, with fewer nonzeros in the factors of the matrix.
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
No journal information available
Organization
No organization information available
Cited Papers
No cited papers available