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

By Stefan Kindermann, Andreas Neubauer. 2008

83 citations recorded by the source corpus.

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 $T$*$T$.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/75d16fb69bcdf29e18b08851467c312d255acfa6

How researchers see this paper

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In Computational Theory and Mathematics

1. Mark A. Lukas
2. Frank Bauer
3. Lorenzo Rosasco

In Mathematical Physics

1. Mark A. Lukas
2. Frank Bauer
3. Lorenzo Rosasco

Citations in the corpus

• Comparing parameter choice methods for regularization of ill-posed problems (2011, background): “some convergence results [88, 111], but no oracle inequalities are known.”