, Volume 40, Issue 2, pp 91–109 | Cite as

A variant of finite-dimensional Tikhonov regularization with a-posteriori parameter choice

  • J. T. King
  • A. Neubauer


In this paper we consider a particular variant of finite-dimensional Tikhonov regularization for ill-posed operator equations. Convergence rates are established and an a-posteriori parameter choice method is derived that leads to optimal convergence rates with respect to data errors and with respect to the finite-dimensional subspace, without using any information about the exact solution. Finally, using linear splines we present several numerical examples that confirm the theoretical results.

AMS Subject Classifications

65R20 45L10 

Key words

Integral equations Tikhonov regularization parameter selection method 

Eine Variante endlich-dimensionaler Tikhonov-Regularisierung mit a-posteriori Parameterwahl


In dieser Arbeit betrachten wir eine besondere Variante endlich-dimensionaler Tikhonov-Regularisierung schlechtgestellter Operatorgleichungen. Konvergenzraten werden nachgewiesen und eine a-posteriori Parameterwahl wird hergeleitet, die optimale Konvergenzraten bezüglich des Datenfehlers und der endlich-dimensionalen Approximation liefert, ohne Information über die exakte Lösung zu benötigen. Schließlich präsentieren wir auch einige numerische Beispiele, bei denen lineare Splinefunktionen verwendet werden, die die theoretischen Ergebnisse bestätigen.


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. T. King
    • 1
  • A. Neubauer
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Institut für MathematikJohannes Kepler UniversitätLinzAustria

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