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On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator

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Abstract

A usual way to characterize the quality of different a posteriori parameter choices is to prove their order-optimality on the different sets of solutions. In paper by Raus and Hämarik (J Inverse Ill-Posed Probl 15(4):419–439, 2007) we introduced the property of the quasi-optimality to characterize the quality of the rule of the a posteriori choice of the regularization parameter for concrete problem Au = f in case of exact operator and discussed the quasi-optimality of different well-known rules for the a posteriori parameter choice as the discrepancy principle, the modification of the discrepancy principle, balancing principle and monotone error rule. In this paper we generalize the concept of the quasi-optimality for the case of a noisy operator and concretize results for the mentioned parameter choice rules.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, J. Liivi 2, 50409, Tartu, Estonia

    Toomas Raus & Uno Hämarik

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  1. Toomas Raus
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  2. Uno Hämarik
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Correspondence to Uno Hämarik.

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Communicated by Yuesheng Xu and Hongqi Yang.

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Raus, T., Hämarik, U. On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator. Adv Comput Math 36, 221–233 (2012). https://doi.org/10.1007/s10444-011-9203-6

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  • DOI: https://doi.org/10.1007/s10444-011-9203-6

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