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RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences

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Abstract

We summarize a recently introduced greedy algorithm for inverse problems in geomathematics. The algorithm is able to combine heterogeneous systems of trial functions to construct a stable approximation to the solution of the given ill-posed problem. The representation of this approximation with respect to the trial functions of mixed types is sparse in the sense that essentially less trial functions than available are used. Some new theoretical results about the method are also proved here.

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Acknowledgements

The support by the German Research Foundation (project number DFG MI 655/7-1) is gratefully acknowledged. Moreover, the author wishes to thank Roger Telschow for proofreading the manuscript.

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Authors and Affiliations

  1. Geomathematics Group, University of Siegen, Siegen, Germany

    Volker Michel

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  1. Volker Michel
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Correspondence to Volker Michel .

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Editors and Affiliations

  1. Geomathematische Gruppe, TU Kaiserslautern FB Mathematik, Kaiserslautern, Germany

    Willi Freeden

  2. University of Central Florida Dept. Mathematics, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Inst. Analysis, TU Braunschweig FB 1 Mathematik und Informatik, Braunschweig, Germany

    Thomas Sonar

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Michel, V. (2013). RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_93-1

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  • DOI: https://doi.org/10.1007/978-3-642-27793-1_93-1

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  • Online ISBN: 978-3-642-27793-1

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