On the Achievable Level of Accuracy for the Solution of Abstract Ill-Posed Problems and Nonlinear Operator Equations in a Banach Space
It has been shown that, for a wide class of ill–posed problems of finding the value of a discontinuous operator by an approximately specified element in a Banach space, the level of accuracy for the resulting solution cannot be higher in order than the level of error in input data. A similar result...
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| Vydáno v: | Russian mathematics Ročník 66; číslo 3; s. 16 - 21 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Moscow
Pleiades Publishing
01.03.2022
Springer Nature B.V |
| Témata: | |
| ISSN: | 1066-369X, 1934-810X |
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| Abstract | It has been shown that, for a wide class of ill–posed problems of finding the value of a discontinuous operator by an approximately specified element in a Banach space, the level of accuracy for the resulting solution cannot be higher in order than the level of error in input data. A similar result is established for a class of nonlinear operator equations with an approximate right side. The classes of problems for which these orders are coincident are specified. |
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| AbstractList | It has been shown that, for a wide class of ill–posed problems of finding the value of a discontinuous operator by an approximately specified element in a Banach space, the level of accuracy for the resulting solution cannot be higher in order than the level of error in input data. A similar result is established for a class of nonlinear operator equations with an approximate right side. The classes of problems for which these orders are coincident are specified. |
| Author | Kokurin, M. Yu Bakushinsky, A. B. |
| Author_xml | – sequence: 1 givenname: M. Yu surname: Kokurin fullname: Kokurin, M. Yu email: kokurinm@yandex.ru organization: Mari State University – sequence: 2 givenname: A. B. surname: Bakushinsky fullname: Bakushinsky, A. B. email: bakush@isa.ru organization: Mari State University, Federal Research Center Computer Science and Control, Institute for Systems Analysis, Russian Academy of Sciences |
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| Cites_doi | 10.3103/S1066369X16100042 10.3103/S1066369X19070016 10.1515/9783110208276 |
| ContentType | Journal Article |
| Copyright | Allerton Press, Inc. 2022. ISSN 1066-369X, Russian Mathematics, 2022, Vol. 66, No. 3, pp. 16–21. © Allerton Press, Inc., 2022. Russian Text © The Author(s), 2022, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, No. 3, pp. 21–27. |
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| Keywords | operator equation accuracy estimate Banach space ill-posed problem |
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| References | BakushinskiiA. B.GoncharskiiA. V.Iterative Methods for Solving Ill-Posed Problems1989MoscowNauka0676.65050 BakushinskiiA. B.KokurinM. Yu.Algorithmic Analysis of Irregular Operator Equations2012MoscowLENAND1247.47054 LeonovA. S.On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problemsRuss. Math.201660232810.3103/S1066369X161000421370.65029 TrenoginV. A.Functional Analysis1980MoscowNauka0517.46001 AgeevA. L.AntonovaT. V.“On ill-posed problems of localization of singularities,” Tr. Inst. Mat. MekhUral. Otd. Ross. Akad. Nauk2011173045 KaltenbacherB.NeubauerA.ScherzerO.Iterative Regularization Methods for Nonlinear Ill–Posed Problems2008BerlinWalter de Gruyter10.1515/97831102082761145.65037 AgeevA. L.AntonovaT. V.Investigation of methods of localization of q-jumps and discontinuities of first kind of noisy functionRuss. Math.20196311110.3103/S1066369X190700161476.65031 A. B. Bakushinskii (10164_CR1) 1989 A. B. Bakushinskii (10164_CR2) 2012 A. L. Ageev (10164_CR4) 2011; 17 A. S. Leonov (10164_CR6) 2016; 60 B. Kaltenbacher (10164_CR3) 2008 A. L. Ageev (10164_CR5) 2019; 63 V. A. Trenogin (10164_CR7) 1980 |
| References_xml | – reference: BakushinskiiA. B.KokurinM. Yu.Algorithmic Analysis of Irregular Operator Equations2012MoscowLENAND1247.47054 – reference: AgeevA. L.AntonovaT. V.“On ill-posed problems of localization of singularities,” Tr. Inst. Mat. MekhUral. Otd. Ross. Akad. Nauk2011173045 – reference: KaltenbacherB.NeubauerA.ScherzerO.Iterative Regularization Methods for Nonlinear Ill–Posed Problems2008BerlinWalter de Gruyter10.1515/97831102082761145.65037 – reference: BakushinskiiA. B.GoncharskiiA. V.Iterative Methods for Solving Ill-Posed Problems1989MoscowNauka0676.65050 – reference: LeonovA. S.On possibility of obtaining linear accuracy evaluation of approximate solutions to inverse problemsRuss. Math.201660232810.3103/S1066369X161000421370.65029 – reference: AgeevA. L.AntonovaT. V.Investigation of methods of localization of q-jumps and discontinuities of first kind of noisy functionRuss. Math.20196311110.3103/S1066369X190700161476.65031 – reference: TrenoginV. A.Functional Analysis1980MoscowNauka0517.46001 – volume: 60 start-page: 23 year: 2016 ident: 10164_CR6 publication-title: Russ. Math. doi: 10.3103/S1066369X16100042 – volume-title: Iterative Methods for Solving Ill-Posed Problems year: 1989 ident: 10164_CR1 – volume-title: Algorithmic Analysis of Irregular Operator Equations year: 2012 ident: 10164_CR2 – volume-title: Functional Analysis year: 1980 ident: 10164_CR7 – volume: 63 start-page: 1 year: 2019 ident: 10164_CR5 publication-title: Russ. Math. doi: 10.3103/S1066369X19070016 – volume-title: Iterative Regularization Methods for Nonlinear Ill–Posed Problems year: 2008 ident: 10164_CR3 doi: 10.1515/9783110208276 – volume: 17 start-page: 30 year: 2011 ident: 10164_CR4 publication-title: Ural. Otd. Ross. Akad. Nauk |
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| SubjectTerms | Banach spaces Ill posed problems Mathematical analysis Mathematics Mathematics and Statistics |
| Title | On the Achievable Level of Accuracy for the Solution of Abstract Ill-Posed Problems and Nonlinear Operator Equations in a Banach Space |
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