Residual norm behavior for Hybrid LSQR regularization

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10468023" target="_blank" >RIV/00216208:11320/23:10468023 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.21136/panm.2022.07" target="_blank" >https://doi.org/10.21136/panm.2022.07</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/panm.2022.07" target="_blank" >10.21136/panm.2022.07</a>

Result language
angličtina
Original language name
Residual norm behavior for Hybrid LSQR regularization
Original language description
Hybrid LSQR represents a powerful method for regularization of large-scale discrete inverse problems, where ill-conditioning of the model matrix and ill-posedness of the problem make the solutions seriously sensitive to the unknown noise in the data. Hybrid LSQR combines the iterative Golub-Kahan bidiagonalization with the Tikhonov regularization of the projected problem. While the behavior of the residual norm for the pure LSQR is well understood and can be used to construct a stopping criterion, this is not the case for the hybrid method. Here we analyze the behavior of norms of approximate solutions and the corresponding residuals in Hybrid LSQR with respect to the Tikhonov regularization parameter. This helps to understand convergence properties of the hybrid approach. Numerical experiments demonstrate the results in finite precision arithmetic.
Czech name
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Czech description
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Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Programs and Algorithms of Numerical Mathematics, Proceedings of Seminar.
ISBN
978-80-85823-73-8
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
65-74
Publisher name
Institute of Mathematics CAS, Prague
Place of publication
Praha
Event location
Jablonec nad Nisou
Event date
Jun 19, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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