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The block Lanczos algorithm for linear ill-posed problems

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Abstract

In the present paper, we propose a new method to inexpensively determine a suitable value of the regularization parameter and an associated approximate solution, when solving ill-conditioned linear system of equations with multiple right-hand sides contaminated by errors. The proposed method is based on the symmetric block Lanczos algorithm, in connection with block Gauss quadrature rules to inexpensively approximate matrix-valued function of the form \(W^Tf(A)W\), where \(W\in {\mathbb {R}}^{n\times k}\), \(k\ll n\), and \(A\in {\mathbb {R}}^{n\times n}\) is a symmetric matrix.

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Acknowledgments

We would like to thank the referee for the pertinent and useful comments towards the improvement of our manuscript.

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Authors and Affiliations

  1. Faculté des Sciences et Techniques-Gueliz, Laboratoire de Mathématiques Appliquées et Informatique, Marrakech, Morocco

    A. H. Bentbib & M. El Guide

  2. Université du Littoral, Côte d’Opale, batiment H. Poincarré, 50 rue F. Buisson, 62280, Calais Cedex, France

    K. Jbilou

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  1. A. H. Bentbib
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  2. M. El Guide
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  3. K. Jbilou
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Correspondence to K. Jbilou.

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Bentbib, A.H., Guide, M.E. & Jbilou, K. The block Lanczos algorithm for linear ill-posed problems. Calcolo 54, 711–732 (2017). https://doi.org/10.1007/s10092-016-0206-z

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