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Titlebook: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization; New Results in Moder Jens Flemming Book 2018

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發(fā)表于 2025-3-21 19:12:44 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
副標(biāo)題New Results in Moder
編輯Jens Flemming
視頻videohttp://file.papertrans.cn/981/980618/980618.mp4
概述Presents recent research results in a consistent notation.Contributes to two very active fields of research.Shows that variational source condition always yields convergence rate results
叢書名稱Frontiers in Mathematics
圖書封面Titlebook: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization; New Results in Moder Jens Flemming Book 2018
描述The book collects and contributes new results on the theory and practice of ill-posed inverse?problems.?.Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are?discussed not only in standard settings but also in situations up to now not covered by the literature.?Especially, ill-posedness of linear operators with uncomplemented null spaces is examined..Tools for convergence rate analysis of regularization methods are extended to a wider field of?applicability. It is shown that the tool known as variational source condition always yields?convergence rate results.?.A theory for nonlinear inverse problems with quadratic structure is developed as well as?corresponding regularization methods. The new methods are applied to a difficult inverse problem?from laser optics..Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive?convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with?sparsity enforcing penalty..
出版日期Book 2018
關(guān)鍵詞inverse problem; ill-posedness; variational source condition; quadratic inverse problem; autoconvolution
版次1
doihttps://doi.org/10.1007/978-3-319-95264-2
isbn_softcover978-3-319-95263-5
isbn_ebook978-3-319-95264-2Series ISSN 1660-8046 Series E-ISSN 1660-8054
issn_series 1660-8046
copyrightSpringer Nature Switzerland AG 2018
The information of publication is updating

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發(fā)表于 2025-3-21 21:59:19 | 只看該作者
Variational Source Conditions and then discuss more or less classical alternatives and their deficiencies. The first of the two main results of this chapter will state that variational source conditions are the right tool for our purposes, and the second demonstrates a way to obtain concrete variational source conditions for qu
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utput routines, the arrangements for calling in various subroutines when required and, above all, the general organization of the problem as a whole. It is an interesting fact that these nonmathematical parts of the program often take many more instructions than the mathematics proper. As an example
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Jens Flemmingaced technology’ because ‘the actual status of the cyborg is murky as to whether it is a metaphor, a dreamlike fantasy and/or a literal being’. In particular, Morse (1998, p. 125) cites the problem of inhabiting both an organic and a virtual body: ‘Travelers on the virtual highways of an information
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em, but computer men felt that this was the way computing ought to go: one might dispense with cards, and overcome many of the problems of man-machine communication. It quickly appeared that, as with computers, there had been a great under- estimation of the amount of work involved, of the difficult
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