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Tikhonov regularization via flexible Arnoldi reduction

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Abstract

Flexible GMRES, introduced by Saad, is a generalization of the standard GMRES method for the solution of large linear systems of equations. It is based on the flexible Arnoldi process for reducing a large square matrix to a small matrix. We describe how the flexible Arnoldi process can be applied to implement one-parameter and multi-parameter Tikhonov regularization of linear discrete ill-posed problems. The method proposed is well suited for large-scale problems. Moreover, computed examples show that our method can give approximate solutions of higher accuracy than available direct methods for small-scale problems.

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Acknowledgments

We would like to thank the referees for comments that lead to improvements of the presentation. This research is supported in part by NSF Grant DMS-1115385.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH, 44242, USA

    Lothar Reichel & Xuebo Yu

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  1. Lothar Reichel
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  2. Xuebo Yu
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Correspondence to Lothar Reichel.

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Communicated by Rosemary Renaut.

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Reichel, L., Yu, X. Tikhonov regularization via flexible Arnoldi reduction. Bit Numer Math 55, 1145–1168 (2015). https://doi.org/10.1007/s10543-014-0542-9

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  • DOI: https://doi.org/10.1007/s10543-014-0542-9

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