Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems

Minimization-based noise level-free parameter choice rules for the selection of the regularization parameter in linear ill-posed problems are studied. convergence results for spectral filter regularization operators using a qualitative condition on the (deterministic) data noise are proven. Furtherm...

Full description

Saved in:
Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 38; p. 233
Main Author Kindermann, Stefan
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.01.2011
Subjects
Convergence (Mathematics)
Functions, Inverse
Linear systems
Parameter estimation
Austria
Online AccessGet full text
ISSN1068-9613
1097-4067

Cover

More Information
Summary:Minimization-based noise level-free parameter choice rules for the selection of the regularization parameter in linear ill-posed problems are studied. convergence results for spectral filter regularization operators using a qualitative condition on the (deterministic) data noise are proven. Furthermore, under source conditions on the exact solution, suboptimal convergence rates and, under certain additional regularity conditions, optimal order convergence rates are shown. The abstract results are examined in more detail for several known parameter choice rules: the quasi-optimality rules (both continuous and discrete) and the Hanke-Raus-rules, together with some specific regularization methods: Tikhonov regularization, Landweber iteration, and spectral cutoff. Key words. regularization, heuristic parameter choice rule, Hanke-Raus rule, quasi-optimality rule, L-curve method
ISSN:1068-9613
1097-4067