Discrepancy Sets for Combined Least Squares Projection and Tikhonov Regularization
To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization. A two-parameter discrepancy principle defines a discrepanc...
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| Published in | Mathematical modelling and analysis Vol. 22; no. 2; pp. 202 - 212 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis
04.03.2017
Vilnius Gediminas Technical University |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1392-6292 1648-3510 1648-3510 |
| DOI | 10.3846/13926292.2017.1289987 |
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| Abstract | To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization. A two-parameter discrepancy principle defines a discrepancy set for any data error bound. The aim of the paper is to describe this set and to indicate its subset such that for regularization parameters from this subset the related regularized solution has the same order of accuracy as the Tikhonov regularization with the standard discrepancy principle but without any discretization. |
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| AbstractList | To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization. A two-parameter discrepancy principle defines a discrepancy set for any data error bound. The aim of the paper is to describe this set and to indicate its subset such that for regularization parameters from this subset the related regularized solution has the same order of accuracy as the Tikhonov regularization with the standard discrepancy principle but without any discretization. To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization. A two-parameter discrepancy principle defines a discrepancy set for any data error bound. The aim of the paper is to describe this set and to indicate its subset such that for regularization parameters from this subset the related regularized solution has the same order of accuracy as the Tikhonov regularization with the standard discrepancy principle but without any discretization.Keywords: linear ill-posed problem, discrepancy principle, LSQ projection, Tikhonov regularization.AMS Subject Classification: 65J20; 47A52; 65F22. |
| Audience | Academic |
| Author | Regińska, Teresa |
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| References | Vainikko G.M. (CIT0020) 1986 Vainikko G. (CIT0019) 1985; 29 CIT0010 CIT0001 Groetsch C.W. (CIT0003) 1984 Hämarik U. (CIT0004) 1992 CIT0011 Morozov V.A. (CIT0012) 1966; 7 Tikhonov A.N. (CIT0017) 1977 Hämarik U. (CIT0005) 1993; 42 Tikhonov A.N. (CIT0018) 1995 Hämarik U. (CIT0006) 2002; 7 CIT0014 CIT0002 CIT0013 CIT0016 CIT0015 CIT0007 CIT0009 CIT0008 |
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| SubjectTerms | discrepancy principle Discretization Least squares Least squares method linear ill-posed problem LSQ projection Mathematical analysis Mathematical models Mathematical research Parameters Projection Regularization Set theory Tikhonov regularization |
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| Title | Discrepancy Sets for Combined Least Squares Projection and Tikhonov Regularization |
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