Publication:
Effective Algorithms for Computing Global and Local Posterior Error Estimates of Solutions to Linear Ill-Posed Problems

Простая страница элемента
dc.contributor.authorLeonov, A. S.
dc.contributor.authorЛеонов, Александр Сергеевич
dc.date.accessioned2024-11-25T17:57:38Z
dc.date.available2024-11-25T17:57:38Z
dc.date.issued2020
dc.description.abstract© 2020, Allerton Press, Inc.We consider extremal problems introduced and investigated earlier by the author for calculating global and local a posteriori error estimates of approximate solutions to ill-posed inverse problems. For linear inverse problems in Hilbert spaces, they consist in maximization of quadratic functionals with two quadratic constraints. The article shows how under certain conditions these problems can be reduced to a problem of maximization of a special (written analytically) differentiable functional with one constraint. New algorithms for calculating global and local a posteriori error estimates based on the solution of these problems are proposed. Their effectiveness is illustrated by numerical experiments on a posteriori error estimation of solutions to the model two-dimensional inverse problem of potential continuation. Experiments show that the proposed algorithms give a posteriori error estimates close to the true error values. Proposed algorithms for global a posteriori error estimation turn out to be more rapid (3 to 5 times) than the previously known algorithms.
dc.format.extentС. 26-34
dc.identifier.citationLeonov, A. S. Effective Algorithms for Computing Global and Local Posterior Error Estimates of Solutions to Linear Ill-Posed Problems / Leonov, A.S. // Russian Mathematics. - 2020. - 64. - № 2. - P. 26-34. - 10.3103/S1066369X20020048
dc.identifier.doi10.3103/S1066369X20020048
dc.identifier.urihttps://www.doi.org/10.3103/S1066369X20020048
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85083062956&origin=resultslist
dc.identifier.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000524245100004
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/20553
dc.relation.ispartofRussian Mathematics
dc.titleEffective Algorithms for Computing Global and Local Posterior Error Estimates of Solutions to Linear Ill-Posed Problems
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue2
oaire.citation.volume64
relation.isAuthorOfPublicationc6afce80-8607-4201-989c-678043775779
relation.isAuthorOfPublication.latestForDiscoveryc6afce80-8607-4201-989c-678043775779
relation.isOrgUnitOfPublicationd19559ab-04cd-486a-ae8e-f40ccd36a1a6
relation.isOrgUnitOfPublication.latestForDiscoveryd19559ab-04cd-486a-ae8e-f40ccd36a1a6
Файлы
Коллекции
Публикации