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Titlebook: Ill-Posed Problems: Theory and Applications; A. Bakushinsky,A. Goncharsky Book 1994 Springer Science+Business Media Dordrecht 1994 Approxi

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發(fā)表于 2025-3-21 17:28:02 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Ill-Posed Problems: Theory and Applications
編輯A. Bakushinsky,A. Goncharsky
視頻videohttp://file.papertrans.cn/462/461171/461171.mp4
叢書名稱Mathematics and Its Applications
圖書封面Titlebook: Ill-Posed Problems: Theory and Applications;  A. Bakushinsky,A. Goncharsky Book 1994 Springer Science+Business Media Dordrecht 1994 Approxi
描述Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill- posed problems in modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill- posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and
出版日期Book 1994
關鍵詞Approximation; Hilbert space; algorithms; functional analysis
版次1
doihttps://doi.org/10.1007/978-94-011-1026-6
isbn_softcover978-94-010-4447-9
isbn_ebook978-94-011-1026-6
copyrightSpringer Science+Business Media Dordrecht 1994
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 20:19:52 | 只看該作者
standable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem compute
板凳
發(fā)表于 2025-3-22 01:24:23 | 只看該作者
Book 1994because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To men
地板
發(fā)表于 2025-3-22 07:51:46 | 只看該作者
Iterative algorithms for solving non-linear ill-posed problems with monotonic operators. Principle mations (see Chapter 3) though being applicable to non-linear case, does not directly lead to numerically implementable RA. This occurs due to additional approximations (usually the iterative ones) which are necessary to calculate values of operators.(or
5#
發(fā)表于 2025-3-22 09:42:12 | 只看該作者
General problems of regularizability,r consists of experimentally observed attributes of the studied phenomena. The problems of processing experimental data are always concerned with inevitable experimental errors. For the purposes of present analysis, we shall consider the objects of the second kind belonging to some metric space ., a
6#
發(fā)表于 2025-3-22 14:22:46 | 只看該作者
,Tikhonov’s scheme for constructing regularizing algorithms,velopment of the numerical methods for solving the ill-posed problems. The constructions described in this chapter immediatly lead to easily implementable numerical algorithms widely used in practice for the linear problems. For the non-linear problems, Tikhonov’s scheme may be used as a principal b
7#
發(fā)表于 2025-3-22 20:07:08 | 只看該作者
Iterative algorithms for solving non-linear ill-posed problems with monotonic operators. Principle ill-posed problems, as well as the regularizing algorithms based on such approximations. The traditional variational technique of constructing approximations (see Chapter 3) though being applicable to non-linear case, does not directly lead to numerically implementable RA. This occurs due to additio
8#
發(fā)表于 2025-3-22 22:29:16 | 只看該作者
Iterative methods for solving non-linear ill-posed operator equations with non-monotonic operators,. The analysis given in this chapter does not use the assumption of monotony. As usual, we concentrate on the cases when the conditions ensuring convergence of traditional iterative techniques are not satisfied.
9#
發(fā)表于 2025-3-23 04:08:25 | 只看該作者
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