Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Toomas Raus"'
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:
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
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
Publikováno v:
jiip. 20:831-854
We consider the Lavrentiev method for the regularization of linear ill-posed problems with noisy data. Classical rules for the choice of the regularization parameter that use the noise level work well for almost exact noise level information, they fa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aa94a3dbd519fceb9ee2f05d9ea1c0bc
https://doi.org/10.1515/jip-2012-0061
https://doi.org/10.1515/jip-2012-0061
Publikováno v:
Journal of Computational and Applied Mathematics. 236(8):2146-2157
We consider Tikhonov regularization of linear ill-posed problems with noisy data. The choice of the regularization parameter by classical rules, such as discrepancy principle, needs exact noise level information: these rules fail in the case of an un
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0aa0f8379b48419a231feab34b40194
Autor:
Uno Hämarik, Toomas Raus
Publikováno v:
Advances in Computational Mathematics. 36:221-233
A usual way to characterize the quality of different a posteriori parameter choices is to prove their order-optimality on the different sets of solutions. In paper by Raus and Hamarik (J Inverse Ill-Posed Probl 15(4):419---439, 2007) we introduced th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::72d81763add7ecd989ef9b7f368b4259
https://doi.org/10.1007/s10444-011-9203-6
https://doi.org/10.1007/s10444-011-9203-6
Publikováno v:
Calcolo. 48:47-59
We consider linear ill-posed problems in Hilbert space with noisy data. The noise level may be given exactly or approximately or there may be no information about the noise level. We regularize the problem using the Landweber method, the Tikhonov met
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0d6d97d9c6b2d1b2cba1dd78293ecd00
https://doi.org/10.1007/s10092-010-0027-4
https://doi.org/10.1007/s10092-010-0027-4