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Full Record Details
Persistent URL
http://purl.org/net/epubs/work/37366454
Record Status
Checked
Record Id
37366454
Title
Sparse stretching for solving sparse-dense linear least-squares problems
Contributors
J Scott (STFC Rutherford Appleton Lab.)
,
M Tuma
Abstract
Large-scale linear least-squares problems arise in a wide range of practical applications. In some cases, the system matrix contains a small number of dense rows. These make the problem significantly harder to solve because their presence limits the direct applicability of sparse matrix techniques. In particular, the normal matrix is (close to) dense, making a Cholesky factorization impractical. One way to help overcome the dense row problem is to employ matrix stretching. Stretching is a sparse matrix technique that improves sparsity by making the least-squares problem larger. We show that standard stretching can still result in the normal matrix for the stretched problem having an unacceptably large amount of fill. This motivates us to propose a new sparse stretching strategy that performs the stretching so as to limit the fill in the normal matrix and its Cholesky factor. Numerical examples from real problems are used to illustrate the potential gains.
Organisation
STFC
,
SCI-COMP
Keywords
Funding Information
Related Research Object(s):
43325330
,
45329722
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Preprint
RAL Preprints
RAL-P-2018-002,
SIAM J Sci Comput
STFC, 2018.
RAL-P-2018-002.pdf
2018
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