Sparse stretching for solving sparse-dense linear least-squares problems

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Persistent URL	http://purl.org/net/epubs/work/37366454
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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
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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