@inproceedings{963ecaac6a724f44b704dd3191d39cd0,
title = "Error Estimation in Ill-Posed Problems in Special Cases",
abstract = "In this review we consider ill-posed inverse problems for linear operator equations Az = u with an operator A acting between two normed spaces. It is well known that, in general, no error estimate can be provided for approximate solution of an ill-posed problem. But in some special cases when we are aware of some a priori information about the unknown exact solution, error estimation can be done. In this paper we review inverse problems on compact sets, as well as inverse problems with source-wise represented solutions. We also touch inverse problems in partially ordered spaces. A posteriori error estimates for regularized solutions with special regularization properties are also discussed here. This work was supported by the Swedish institute (Visby program) and the RFBR grants 11-01-0040_a and 12-01-00524_a.",
keywords = "A posteriori error estimation, Ill-posed problems, Regularizing algorithms",
author = "Yagola, {Anatoly G.} and Korolev, {Yury M.}",
year = "2013",
month = jan,
day = "1",
doi = "10.1007/978-1-4614-7816-4_9",
language = "English",
isbn = "9781461478157",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York",
pages = "155--164",
editor = "L. Beilina",
booktitle = "Applied Inverse Problems - Select Contributions from the First Annual Workshop on Inverse Problems",
address = "USA United States",
note = "1st Annual Workshop on Inverse Problems ; Conference date: 02-06-2011 Through 03-06-2011",
}