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Full Record Details
Persistent URL
http://purl.org/net/epubs/work/12194841
Record Status
Checked
Record Id
12194841
Title
Preconditioning of linear least-squares problems by identifying basic variables
Contributors
M Arioli (Rutherford Appleton Lab.)
,
IS Duff (Rutherford Appleton Lab.)
Abstract
The preconditioning of linear least-squares problems is a hard task. The linear model underpinning least-squares problems, that is the overdetermined matrix defining it, does not have the properties of differential problems that make standard preconditioners effective. Incomplete Cholesky techniques applied to the normal equations do not produce a well conditioned problem. We attempt to remove the ill-conditioning by identifying a subset of rows and columns in the overdetermined matrix defining the linear model that identifes the best conditioned basic variables matrix. We then compute a symmetric quasi-definite linear system having a condition number depending solely on the geometry of the non-basic variables and that is independent of the original condition number. We illustrate the performance of our approach on some standard test problems and show it is competitive with other approaches.
Organisation
STFC
,
SCI-COMP
,
SCI-COMP-CM
Keywords
LSQR;
,
sparse LU factorization;
,
preconditioning;
,
linear least squares;
,
sparse rectangular matrices;
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Preprints
RAL-P-2014-007. 2014.
RAL-P-2014-007.pdf
2014
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