Complexity Estimates for Severely Ill-posed Problems under A Posteriori Selection of Regularization Parameter
In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepan...
Ausführliche Beschreibung
Autor*in: |
Sergii G. Solodky [verfasserIn] Ganna L. Myleiko [verfasserIn] Evgeniya V. Semenova [verfasserIn] |
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Sprache: |
Englisch |
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2017 |
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Übergeordnetes Werk: |
In: Mathematical Modelling and Analysis - Vilnius Gediminas Technical University, 2018, 22(2017), 3 |
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Übergeordnetes Werk: |
volume:22 ; year:2017 ; number:3 |
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DOI / URN: |
10.3846/13926292.2017.1307284 |
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Katalog-ID: |
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10.3846/13926292.2017.1307284 doi (DE-627)DOAJ00644735X (DE-599)DOAJ545771421dfa4b1da7d55c25e8e35596 DE-627 ger DE-627 rakwb eng QA1-939 Sergii G. Solodky verfasserin aut Complexity Estimates for Severely Ill-posed Problems under A Posteriori Selection of Regularization Parameter 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepancy and balancing principles. It is established that proposed strategies not only achieved optimal order of accuracy on the class of problems under consideration, but also they are economical in the sense of used discrete information. severely ill-posed problem complexity Galerkin’s information discrepancy principle balancing principle Mathematics Ganna L. Myleiko verfasserin aut Evgeniya V. Semenova verfasserin aut In Mathematical Modelling and Analysis Vilnius Gediminas Technical University, 2018 22(2017), 3 (DE-627)638410843 (DE-600)2578803-6 16483510 nnns volume:22 year:2017 number:3 https://doi.org/10.3846/13926292.2017.1307284 kostenfrei https://doaj.org/article/545771421dfa4b1da7d55c25e8e35596 kostenfrei https://journals.vgtu.lt/index.php/MMA/article/view/896 kostenfrei https://doaj.org/toc/1392-6292 Journal toc kostenfrei https://doaj.org/toc/1648-3510 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 22 2017 3 |
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10.3846/13926292.2017.1307284 doi (DE-627)DOAJ00644735X (DE-599)DOAJ545771421dfa4b1da7d55c25e8e35596 DE-627 ger DE-627 rakwb eng QA1-939 Sergii G. Solodky verfasserin aut Complexity Estimates for Severely Ill-posed Problems under A Posteriori Selection of Regularization Parameter 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepancy and balancing principles. It is established that proposed strategies not only achieved optimal order of accuracy on the class of problems under consideration, but also they are economical in the sense of used discrete information. severely ill-posed problem complexity Galerkin’s information discrepancy principle balancing principle Mathematics Ganna L. Myleiko verfasserin aut Evgeniya V. Semenova verfasserin aut In Mathematical Modelling and Analysis Vilnius Gediminas Technical University, 2018 22(2017), 3 (DE-627)638410843 (DE-600)2578803-6 16483510 nnns volume:22 year:2017 number:3 https://doi.org/10.3846/13926292.2017.1307284 kostenfrei https://doaj.org/article/545771421dfa4b1da7d55c25e8e35596 kostenfrei https://journals.vgtu.lt/index.php/MMA/article/view/896 kostenfrei https://doaj.org/toc/1392-6292 Journal toc kostenfrei https://doaj.org/toc/1648-3510 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 22 2017 3 |
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Complexity Estimates for Severely Ill-posed Problems under A Posteriori Selection of Regularization Parameter |
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In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepancy and balancing principles. It is established that proposed strategies not only achieved optimal order of accuracy on the class of problems under consideration, but also they are economical in the sense of used discrete information. |
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In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepancy and balancing principles. It is established that proposed strategies not only achieved optimal order of accuracy on the class of problems under consideration, but also they are economical in the sense of used discrete information. |
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In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization. To select a regularization parameter we employ two different a posteriori rules, namely, discrepancy and balancing principles. It is established that proposed strategies not only achieved optimal order of accuracy on the class of problems under consideration, but also they are economical in the sense of used discrete information. |
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|
score |
7.401019 |