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Inheritance of the discrete Picard condition in Krylov subspace methods

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Abstract

When projection methods are employed to regularize linear discrete ill-posed problems, one implicitly assumes that the discrete Picard condition (DPC) is somehow inherited by the projected problems. In this paper we show that, under some assumptions, the DPC holds for the projected uncorrupted systems computed by various Krylov subspace methods. By exploiting the inheritance of the DPC, some estimates on the behavior of the projected problems are also derived. Numerical examples are provided in order to illustrate the accuracy of the derived estimates.

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Acknowledgments

We are grateful to the anonymous Referee and to the Editor for providing insightful suggestions that helped to expand and improve the paper.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Padova, Via Trieste 63, Padova, Italy

    Silvia Gazzola

  2. Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Valerio 12/1, Trieste, Italy

    Paolo Novati

Authors
  1. Silvia Gazzola
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  2. Paolo Novati
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Corresponding author

Correspondence to Silvia Gazzola.

Additional information

Communicated by Michiel Hochstenbach.

This work was partially supported by MIUR (Project PRIN 2012 N. 2012MTE38N), and by the University of Padova (Project CPDA124755 “Multivariate approximation with applications to image reconstruction”).

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Gazzola, S., Novati, P. Inheritance of the discrete Picard condition in Krylov subspace methods. Bit Numer Math 56, 893–918 (2016). https://doi.org/10.1007/s10543-015-0578-5

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