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LU Preconditioning for Overdetermined Sparse Least Squares Problems

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Parallel Processing and Applied Mathematics (PPAM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9573))

Abstract

We investigate how to use an LU factorization with the classical lsqr routine for solving overdetermined sparse least squares problems. Usually L is much better conditioned than A and iterating with L instead of A results in faster convergence. When a runtime test indicates that L is not sufficiently well-conditioned, a partial orthogonalization of L accelerates the convergence. Numerical experiments illustrate the good behavior of our algorithm in terms of storage and convergence.

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Author information

Authors and Affiliations

  1. North Carolina State University, Raleigh, USA

    Gary W. Howell

  2. Université Paris-Sud and Inria, Orsay, France

    Marc Baboulin

Authors
  1. Gary W. Howell
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  2. Marc Baboulin
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Corresponding author

Correspondence to Gary W. Howell .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Howell, G.W., Baboulin, M. (2016). LU Preconditioning for Overdetermined Sparse Least Squares Problems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2015. Lecture Notes in Computer Science(), vol 9573. Springer, Cham. https://doi.org/10.1007/978-3-319-32149-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-32149-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32148-6

  • Online ISBN: 978-3-319-32149-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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