Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Uno Hämarik"'
Autor:
Toomas Raus, Uno Hämarik
Publikováno v:
Mathematics, Vol 8, Iss 7, p 1166 (2020)
We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the global mi
Externí odkaz:
https://doaj.org/article/4a4c4d36752c41f3ba88f362fc4d3298
Publikováno v:
Mathematical Modelling and Analysis, Vol 15, Iss 1 (2010)
We consider regularization of linear ill‐posed problem Au = f with noisy data fδ, ¦fδ - f¦≤ δ . The approximate solution is computed as the extrapolated Tikhonov approximation, which is a linear combination of n ≥ 2 Tikhonov approximations
Externí odkaz:
https://doaj.org/article/aa47e857df4a4b79a809357500b92060
Autor:
Toomas Raus, Uno Hämarik
Publikováno v:
Mathematical Modelling and Analysis, Vol 14, Iss 2 (2009)
We propose a new a posteriori rule for choosing the regularization parameter α in (iterated) Tikhonov method for solving linear ill‐posed problems in Hilbert spaces. We assume that data are noisy but noise level δ is given. We prove that (iterate
Externí odkaz:
https://doaj.org/article/47893f9c90fb46a1a7c8089baf454610
Autor:
Toomas Raus, Uno Hämarik
Publikováno v:
Mathematical Modelling and Analysis, Vol 14, Iss 1 (2009)
We consider linear ill‐posed problems in Hilbert spaces with noisy right hand side and given noise level. For approximation of the solution the Tikhonov method or the iterated variant of this method may be used. In self‐adjoint problems the Lavre
Externí odkaz:
https://doaj.org/article/23dcc6f022c64c3f9cc78faccc4c4dec
Autor:
Uno Hämarik, Reimo Palm
Publikováno v:
Mathematical Modelling and Analysis, Vol 12, Iss 1 (2007)
We consider stopping rules in conjugate gradient type iteration methods for solving linear ill‐posed problems with noisy data. The noise level may be known exactly or approximately or be unknown. We propose several new stopping rules, mostly for th
Externí odkaz:
https://doaj.org/article/9421b54555354ba9a80033a72043575e
Publikováno v:
Journal of Inverse and Ill-posed Problems. 27:117-131
We study the choice of the regularisation parameter for linear ill-posed problems in the presence of data noise and operator perturbations, for which a bound on the operator error is known but the data noise-level is unknown. We introduce a new famil
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0beb86debec785821cae27dbceec10a
https://doi.org/10.1515/jiip-2018-0062
https://doi.org/10.1515/jiip-2018-0062
Autor:
Toomas Raus, Uno Hämarik
Publikováno v:
Trends in Mathematics ISBN: 9783319708232
We consider choice of the regularization parameter in Tikhonov method in the case of the unknown noise level of the data. From known heuristic parameter choice rules often the best results were obtained in the quasi-optimality criterion where the par
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2d8aa30fcb47ecb47466a8c63d6482c1
https://doi.org/10.1007/978-3-319-70824-9_12
https://doi.org/10.1007/978-3-319-70824-9_12
Autor:
Urve Kangro, Uno Hämarik
Publikováno v:
Trends in Mathematics ISBN: 9783319708232
We consider ill-posed linear operator equations with operators acting between Banach spaces. For the stable solution of ill-posed problems regularization is necessary, and for using computers discretization is necessary. In some cases discretization
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1eaa9a424316a06b4e13adf3b3a9307d
https://doi.org/10.1007/978-3-319-70824-9_5
https://doi.org/10.1007/978-3-319-70824-9_5
Publikováno v:
Numerical Functional Analysis and Optimization. 34:1370-1417
The focus of this paper is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1932737e9f608695256538bd9cc7424b
https://doi.org/10.1080/01630563.2013.819515
https://doi.org/10.1080/01630563.2013.819515
Publikováno v:
Inverse Problems in Science and Engineering. 22:10-30
We consider an ill-posed equation in a Hilbert space with a noisy operator and a noisy right-hand side. The noise level information is given in a general form, as a norm of a certain operator applied to the noise. We derive the monotone error rule (M
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9e62da7014b0c476c3a95ff8d2aac79e
https://doi.org/10.1080/17415977.2013.827185
https://doi.org/10.1080/17415977.2013.827185