# American Institute of Mathematical Sciences

May  2008, 2(2): 291-299. doi: 10.3934/ipi.2008.2.291

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

 1 Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz, Austria 2 Industrial Mathematics Institute, Johannes Kepler University Linz A-4040 Linz, Austria

Received  December 2007 Revised  March 2008 Published  April 2008

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 $T$*$T$.
Citation: Stefan Kindermann, Andreas Neubauer. On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization. Inverse Problems & Imaging, 2008, 2 (2) : 291-299. doi: 10.3934/ipi.2008.2.291
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