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Error estimates for linear systems with applications to regularization

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Abstract

In this paper, we discuss several (old and new) estimates for the norm of the error in the solution of systems of linear equations, and we study their properties. Then, these estimates are used for approximating the optimal value of the regularization parameter in Tikhonov’s method for ill-conditioned systems. They are also used as a stopping criterion in iterative methods, such as the conjugate gradient algorithm, which have a regularizing effect. Several numerical experiments and comparisons with other procedures show the effectiveness of our estimates.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, UMR CNRS 8524, Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Ascq Cedex, France

    C. Brezinski

  2. Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123, Cagliari, Italy

    G. Rodriguez & S. Seatzu

Authors
  1. C. Brezinski
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  2. G. Rodriguez
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  3. S. Seatzu
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Corresponding author

Correspondence to G. Rodriguez.

Additional information

This work was supported by MIUR under the PRIN grant no. 2006017542-003, and the University of Cagliari.

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Brezinski, C., Rodriguez, G. & Seatzu, S. Error estimates for linear systems with applications to regularization. Numer Algor 49, 85–104 (2008). https://doi.org/10.1007/s11075-008-9163-1

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  • DOI: https://doi.org/10.1007/s11075-008-9163-1

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