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

Stefan Kindermann; Andreas Neubauer

doi:10.3934/ipi.2008.2.291

Article Contents

2008, Volume 2, Issue 2: 291-299. Doi: 10.3934/ipi.2008.2.291

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

Stefan Kindermann^1, and
Andreas Neubauer^2,

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

Received: November 30, 2007

Revised: February 29, 2008

Published: April 2008

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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.

Citation:

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References

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