NDLI: Preconditioned Iterative Methods for Solving Linear Least Squares Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tůma, Miroslav Mas, José Marín, José Bru, Rafael
Copyright Year	2014
Abstract	New preconditioning strategies for solving $m \times n$ overdetermined large and sparse linear least squares problems using the conjugate gradient for least squares (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 $n \times n$ 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.
Starting Page	A2002
Ending Page	A2022
Page Count	21
File Format	PDF
ISSN	10648275
DOI	10.1137/130931588
e-ISSN	10957197
Issue Number	4
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-08-19
Access Restriction	Subscribed
Subject Keyword	incomplete decompositions Factorization of matrices Overdetermined systems, pseudoinverses Linear equations preconditioned iterative methods Sparse matrices linear least squares approximate inverses
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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