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Extrapolation techniques for ill-conditioned linear systems

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Summary.

In this paper, the regularized solutions of an ill–conditioned system of linear equations are computed for several values of the regularization parameter \(\lambda\). Then, these solutions are extrapolated at \(\lambda=0\) by various vector rational extrapolations techniques built for that purpose. These techniques are justified by an analysis of the regularized solutions based on the singular value decomposition and the generalized singular value decomposition. Numerical results illustrate the effectiveness of the procedures.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique et d'Optimisation, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq cedex, France , , , , , , FR

    C. Brezinski

  2. Dipartimento di Elettronica e Informatica, Università degli Studi di Padova, via Gradenigo 6/a, 35131 Padova, Italy , , , , , , IT

    M. Redivo–Zaglia

  3. Dipartimento di Matematica, Università degli Studi di Cagliari, Viale Merello 92, 09123, Cagliari, Italy (e-mail: rodriguez@unica.it, seatzu@unica.it) , , , , , , IT

    G. Rodriguez & S. Seatzu

Authors
  1. C. Brezinski
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  2. M. Redivo–Zaglia
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  3. G. Rodriguez
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  4. S. Seatzu
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Received June 23, 1997 / Revised version received October 24, 1997

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Brezinski, C., Redivo–Zaglia, M., Rodriguez, G. et al. Extrapolation techniques for ill-conditioned linear systems. Numer. Math. 81, 1–29 (1998). https://doi.org/10.1007/s002110050382

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  • DOI: https://doi.org/10.1007/s002110050382

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