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Optimisation in the regularisation ill-posed problems

Published online by Cambridge University Press:  17 February 2009

A. R. Davies  and
R. S. Anderssen
A. R. Davies
Affiliation:
Department of Applied Mathematics, University College of Wales, Aberystyth SY23 3BZ, United Kingdom.
R. S. Anderssen
Affiliation:
Division of Mathematics and Statistics, C.S.I.R. O., P. O. Box 1965, Canberra City, A.C.T. 2601, Australia.
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We survey the role played by optimization in the choice of parameters for Tikhonov regularization of first-kind integral equations. Asymptotic analyses are presented for a selection of practical optimizing methods applied to a model deconvolution problem. These methods include the discrepancy principle, cross-validation and maximum likelihood. The relationship between optimality and regularity is emphasized. New bounds on the constants appearing in asymptotic estimates are presented.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 114 - 133
Copyright
Copyright © Australian Mathematical Society 1986

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