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Inverse Problems and Imaging (IPI)
 

On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization

Pages: 291 - 299, Volume 2, Issue 2, May 2008

doi:10.3934/ipi.2008.2.291       Abstract        References        Full Text (145.3K)       Related Articles

Stefan Kindermann - Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz, Austria (email)
Andreas Neubauer - Industrial Mathematics Institute, Johannes Kepler University Linz A-4040 Linz, Austria (email)

Abstract: In this paper we derive convergence and convergence rates results of the quasioptimality criterion for (iterated) Tikhonov regularization. We prove convergence and suboptimal rates under a qualitative condition on the decay of the noise with respect to the spectral family of $T$$T$*. Moreover, optimal rates are obtained if the exact solution satisfies a decay condition with respect to the spectral family of $T$*$T$.

Keywords:  Quasioptimality criterion, heuristic parameter selection.
Mathematics Subject Classification:  47A52.

Received: December 2007;      Revised: March 2008;      Published: April 2008.

 References