A rational Arnoldi approach for ill-conditioned linear systems

Authors:
C. Brezinski;P. Novati;M. Redivo-Zaglia
Affiliations:
Laboratoire Paul Painlevé, UMR CNRS 8524, UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq cedex, France;Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121 Padova, Italy;Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121 Padova, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense, the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equations and interpolation theory are presented. Finally, the method is extended to work in connection with the standard Tikhonov regularization with the right-hand side contaminated by noise.