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Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

SYSNO ASEP	0432761
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems
Author(s)	Bru, R. (ES) Marín, J. (ES) Mas, J. (ES) Tůma, Miroslav (UIVT-O)_{SAI, RID, ORCID}
Source Title	SIAM Journal on Scientific Computing. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1064-8275 Roč. 36, č. 4 (2014), A2002-A2022
Number of pages	21 s.
Language	eng - English
Country	US - United States
Keywords	preconditioned iterative methods ; incomplete decompositions ; approximate inverses ; linear least squares
Subject RIV	BA - General Mathematics
Institutional support	UIVT-O - RVO:67985807
UT WOS	000344743800028
EID SCOPUS	84987652818
DOI	10.1137/130931588
Annotation	New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU factors of an n × n submatrix of the system matrix is our second approach. A new way to find this submatrix based on a specific weighted transversal problem is proposed. Numerical experiments demonstrate different algebraic and implementational features of the new approaches and put them into the context of current progress in preconditioning of CGLS. It is shown, in particular, that the robustness demonstrated earlier by the BIF preconditioning strategy transfers into the linear least squares solvers and the use of the weighted transversal helps to improve the LU-based approach.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2015

Number of the records: 1