Regularization parameter estimation for large-scale Tikhonov regularization using a priori information

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10051684" target="_blank" >RIV/00216208:11320/10:10051684 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Regularization parameter estimation for large-scale Tikhonov regularization using a priori information
Original language description
This paper is concerned with estimating the solutions of numerically ill-posed least squares problems through Tikhonov regularization. Given apriori estimates on the covariance structure of errors in the measurement data b, and a suitable statistically-chosen regularization parameter, the Tikhonov regularized least squares functional J approximately follows a chi2 distribution with M degrees of freedom. Using the generalized singular value decomposition a regularization parameter can then be found suchthat the resulting J follows this chi2 distribution, see Mead and Renaut (2008). Because the algorithm explicitly relies on the direct solution of the problem obtained using the generalized singular value decomposition it is not practical for large scaleproblems. Here the approach is extended for large scale problems through the use of the Newton iteration in combination with a Golub-Kahan iterative bidiagonalization of the regularized problem.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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