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Convergence Rates Results for Iterative Methods for Solving Nonlinear Ill-Posed Problems

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Surveys on Solution Methods for Inverse Problems

Abstract

The growth of the area of inverse problems within applied mathematics in recent years has been driven both by the needs of applications and by advances in a rigorous convergence theory of regularization methods for the solution of nonlinear ill-posed problems. There are at least two widely used approaches for solving inverse problems in a stable way: Tikhonov regularization and iterative regularization techniques. In this paper we give an overview over the latter. Moreover, we put the analysis of iterative methods for the solution of ill-posed problems into perspective with the analysis of iterative methods for the solution of well-posed problems.

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Authors and Affiliations

  1. Industrial Mathematics Institute, Johannes Kepler Universität, Altenberger Str. 69, A-4040, Linz, Austria

    H. W. Engl & O. Scherzer

Authors
  1. H. W. Engl
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  2. O. Scherzer
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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    David Colton

  2. Institut für Mathematik, Johannes-Kepler-Universität, Linz, Austria

    Heinz W. Engl

  3. Fachbereich Mathematik, Universität des Saarlandes, Saarbrücken, Federal Republic of Germany

    Alfred K. Louis

  4. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York, USA

    Joyce R. McLaughlin

  5. Department of Mathematics, Texas A & M University, College Station, Texas, USA

    William Rundell

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© 2000 Springer-Verlag/Wien

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Engl, H.W., Scherzer, O. (2000). Convergence Rates Results for Iterative Methods for Solving Nonlinear Ill-Posed Problems. In: Colton, D., Engl, H.W., Louis, A.K., McLaughlin, J.R., Rundell, W. (eds) Surveys on Solution Methods for Inverse Problems. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6296-5_2

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  • DOI: https://doi.org/10.1007/978-3-7091-6296-5_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83470-1

  • Online ISBN: 978-3-7091-6296-5

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