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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 such that 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 scale problems. 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. 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 such that 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 scale problems. 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. (en)
Title	Regularization parameter estimation for large-scale Tikhonov regularization using a priori information Regularization parameter estimation for large-scale Tikhonov regularization using a priori information (en)
skos:prefLabel	Regularization parameter estimation for large-scale Tikhonov regularization using a priori information Regularization parameter estimation for large-scale Tikhonov regularization using a priori information (en)
skos:notation	RIV/00216208:11320/10:10051684!RIV11-MSM-11320___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	12
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Hnětynková, Iveta
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	284500
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/10:10051684
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Newton algorithm; hybrid methods; Golub-Kahan iterative bidiagonalization; chi2-distribution; Tikhonov regularization; ill-posed problems (en)
http://linked.open.../riv/klicoveSlovo	hybrid methods ill-posed problems Golub-Kahan iterative bidiagonalization Newton algorithm Tikhonov regularization chi2-distribution
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[44A9E425A87A]
http://linked.open...i/riv/nazevZdroje	Computational Statistics and Data Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	54
http://linked.open...iv/tvurceVysledku	Hnětynková, Iveta Mead, Jodi Renaut, Rosemary
http://linked.open...ain/vavai/riv/wos	000281333900047
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0167-9473
number of pages	16 (xsd:int)
http://localhost/t...ganizacniJednotka	11320
is http://linked.open...avai/riv/vysledek of	Regularization parameter estimation for large-scale Tikhonov regularization using a priori information Regularization parameter estimation for large-scale Tikhonov regularization using a priori information Regularization parameter estimation for large-scale Tikhonov regularization using a priori information

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