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A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems

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Summary

In this paper we study a multi-grid method for the numerical solution of nonlinear systems of equations arising from the discretization of ill-posed problems, where the special eigensystem structure of the underlying operator equation makes it necessary to use special smoothers. We provide uniform contraction factor estimates and show that a nested multigrid iteration together with an a priori or a posteriori chosen stopping index defines a regularization method for the ill-posed problem, i.e., a stable solution method, that converges to an exact solution of the underlying infinite-dimensional problem as the data noise level goes to zero, with optimal rates under additional regularity conditions.

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Authors and Affiliations

  1. Industrial Mathematics Institute, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Barbara Kaltenbacher

  2. Research Institute for Symbolic Computation, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Josef Schicho

Authors
  1. Barbara Kaltenbacher
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  2. Josef Schicho
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Supported by the Fonds zur Förderung der wissenschaftlichen Forschung under grant T 7-TEC and project F1308 within Spezialforschungsbereich 13

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Kaltenbacher, B., Schicho, J. A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems. Numer. Math. 93, 77–107 (2002). https://doi.org/10.1007/BF02679438

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  • DOI: https://doi.org/10.1007/BF02679438

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