Skip to main content
SpringerLink
Log in
Book cover

Modelling and Inverse Problems of Control for Distributed Parameter Systems pp 81–92Cite as

Convergence rates for regularized nonlinear illposed problems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 154))

Abstract

Convergence and rate of convergence are studied for nonlinear illposed inverse problems that are stabilized by means of Tikhonov regularization while the parameter space as well as the parameter-to-output mapping are discretized. The theoretical results are illustrated by means of numerical examples.

Supported in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under S3206.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, 1989.

    Google Scholar 

  2. H.W. Engl, K. Kunisch and A. Neubauer, Tikhonov regularization for the solution of nonlinear ill-posed problems, Inverse Problems 5 (1989), 523–540.

    Google Scholar 

  3. G. Geymayer, Regularisierungsverfahren und deren Anwendung auf Inverse Randwertprobleme, Diplomarbeit, Technical University of Graz, 1988.

    Google Scholar 

  4. C.W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind, Pitman, Boston, 1984.

    Google Scholar 

  5. G. Geymayer and K. Kunisch, Convergence rates for regularized illposed problems, Technical Report at Technical University of Graz.

    Google Scholar 

  6. K. Kunisch and L. White, Regularity properties in parameter estimation of diffusion coefficients in elliptic boundary value problems, Appl. Analysis, 21 (1986), 71–87.

    Google Scholar 

  7. V.A. Morozov, Methods for Solving Incorrectly Posed Problems, Springer Verlag, New York, 1984.

    Google Scholar 

  8. V. Mosco, Convergence of convex sets and solutions of variational inequalities, Adv. Math. 3 (1969), 510–585.

    Google Scholar 

  9. A. Neubauer, Tikhonov regularization for non-linear illposed problems: optimal convergence rates and finite dimensional approximation, Inverse Problems 5 (1989), 541–558.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Graz, A-8010, Graz, Austria

    K. Kunisch & G. Geymayer

Authors
  1. K. Kunisch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Geymayer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alexander Kurzhanski Irena Lasiecka

Rights and permissions

Reprints and permissions

Copyright information

© 1991 International Federation for Information Processing

About this paper

Cite this paper

Kunisch, K., Geymayer, G. (1991). Convergence rates for regularized nonlinear illposed problems. In: Kurzhanski, A., Lasiecka, I. (eds) Modelling and Inverse Problems of Control for Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044485

Download citation

  • DOI: https://doi.org/10.1007/BFb0044485

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53583-6

  • Online ISBN: 978-3-540-46839-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation