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On the choice of solution subspace for nonstationary iterated Tikhonov regularization

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Abstract

Tikhonov regularization is a popular method for the solution of linear discrete ill-posed problems with error-contaminated data. Nonstationary iterated Tikhonov regularization is known to be able to determine approximate solutions of higher quality than standard Tikhonov regularization. We investigate the choice of solution subspace in iterative methods for nonstationary iterated Tikhonov regularization of large-scale problems. Generalized Krylov subspaces are compared with Krylov subspaces that are generated by Golub–Kahan bidiagonalization and the Arnoldi process. Numerical examples illustrate the effectiveness of the methods.

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Authors and Affiliations

  1. Geomathematics Key Laboratory of Sichuan, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China

    Guangxin Huang & Feng Yin

  2. College of Management Science, Chengdu University of Technology, Chengdu, 610059, People’s Republic of China

    Guangxin Huang

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

    Lothar Reichel

  4. School of Sciences, Sichuan University of Science and Engineering, Zigong, 643000, People’s Republic of China

    Feng Yin

Authors
  1. Guangxin Huang
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  2. Lothar Reichel
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  3. Feng Yin
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Correspondence to Lothar Reichel.

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Dedicated to Gerhard Opfer on the occasion of his 80th birthday.

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Huang, G., Reichel, L. & Yin, F. On the choice of solution subspace for nonstationary iterated Tikhonov regularization. Numer Algor 72, 1043–1063 (2016). https://doi.org/10.1007/s11075-015-0079-2

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  • DOI: https://doi.org/10.1007/s11075-015-0079-2

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