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Augmented Subspaces in the LSQR Krylov Method

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Abstract

The LSQR iterative method is a Krylov subspace method for solving least-squares problems. Early termination is rare, and it is common for LSQR to require many iterations before an approximation of the solution with desired accuracy has been determined. In this paper, we present a restarted LSQR method and we use a new technique for accelerating the convergence of restated by adding some approximate error vectors to the Krylov subspace. The effectiveness of the new method is illustrated by several examples.

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Acknowledgements

We would like to thank the referees for their valuable remarks and helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Science and Computer, Kharazmi University, Tehran, Iran

    Zahra Asgari & Esmail Babolian

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Faezeh Toutounian

Authors
  1. Zahra Asgari
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  2. Faezeh Toutounian
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  3. Esmail Babolian
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Correspondence to Faezeh Toutounian.

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Asgari, Z., Toutounian, F. & Babolian, E. Augmented Subspaces in the LSQR Krylov Method. Iran J Sci Technol Trans Sci 44, 1661–1665 (2020). https://doi.org/10.1007/s40995-020-01002-2

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  • DOI: https://doi.org/10.1007/s40995-020-01002-2

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