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Full Record Details
Persistent URL
http://purl.org/net/epubs/work/24428477
Record Status
Checked
Record Id
24428477
Title
Numerically-aware orderings for sparse symmetric linear systems
Contributors
JD Hogg (STFC Rutherford Appleton Lab.)
,
JA Scott (STFC Rutherford Appleton Lab.)
,
HS Thorne (STFC Rutherford Appleton Lab.)
Abstract
Sparse symmetric indefinite problems arise in a large number of important application areas; they are often solved through the use of an LDLT factorization via a sparse direct solver. Whilst for many problems, prescaling the system matrix A is sufficient to maintain stability of the factorization, for a small but important fraction of problems numerical pivoting is required. Pivoting often incurs a significant overhead and consequently a number of techniques have been proposed to try and limit the need for pivoting. In particular, numerically-aware ordering algorithms may be used, that is, orderings that depend not only on the sparsity pattern of A but also on the values of its (scaled) entries. Current approaches identify large entries of A and symmetrically permute them onto the subdiagonal where they can be used as part of a 2 2 pivot. This is numerically effective, but the fill in the factor L and hence the runtime of the factorization and subsequent triangular solves may be significantly increased over a standard ordering if no pivoting is required. We present a new algorithm that combines a matching-based approach with a numerically- aware nested dissection ordering. Numerical comparisons with current approaches for some tough symmetric indefinite problems are given.
Organisation
STFC
,
SCI-COMP
,
SCI-COMP-CM
Keywords
sparse symmetric matrices
,
sparse matrix ordering
,
nested dissection
,
sparse direct methods
,
numerically aware ordering
Funding Information
EPSRC
(EP/M025179/1)
Related Research Object(s):
25845401
,
35371260
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Preprint
RAL Preprints
RAL-P-2016-004,
ACM Trans Math Software
2016.
RAL-P-2016-004.pdf
2016
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