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Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

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    0432761 - ÚI 2015 RIV US eng J - Journal Article
    Bru, R. - Marín, J. - Mas, J. - Tůma, Miroslav
    Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems.
    SIAM Journal on Scientific Computing. Roč. 36, č. 4 (2014), A2002-A2022. ISSN 1064-8275. E-ISSN 1095-7197
    Institutional support: RVO:67985807
    Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares
    Subject RIV: BA - General Mathematics
    Impact factor: 1.854, year: 2014

    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.
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