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A parameter choice strategy for the inversion of multiple observations

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Abstract

In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate strategies are required to choose a set of ‘good’ parameters. In this study, we present a fairly general method for choosing such a set of parameters, provided that discrete direct, but maybe noisy, measurements of the underlying quantity are included in the observation data, and the inner product of the reconstruction space can be accurately estimated by the inner product of the discretization space. Then the proposed parameter choice method gives an accuracy that only by an absolute constant multiplier differs from the noise level and the accuracy of the best approximant in the reconstruction and in the discretization spaces.

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Authors and Affiliations

  1. Computational Science Center, University of Vienna, Oskar Morgenstern Platz 1, 1090, Vienna, Austria

    Christian Gerhards

  2. Department of Mathematics, University of Innsbruck, Technikerstraβe 13, 6020, Innsbruck, Austria

    Sergiy Pereverzyev Jr.

  3. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria

    Pavlo Tkachenko

Authors
  1. Christian Gerhards
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  2. Sergiy Pereverzyev Jr.
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  3. Pavlo Tkachenko
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Corresponding author

Correspondence to Pavlo Tkachenko.

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Communicated by: Jan Hesthaven.

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Gerhards, C., Pereverzyev, S. & Tkachenko, P. A parameter choice strategy for the inversion of multiple observations. Adv Comput Math 43, 101–112 (2017). https://doi.org/10.1007/s10444-016-9477-9

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  • DOI: https://doi.org/10.1007/s10444-016-9477-9

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