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Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803
The authors study the best possible accuracy of recovering the solution from linear ill-posed problems in variable Hilbert scales. A priori smoothness of the solution is expressed in terms of generalExpand
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Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations
Abstract. We consider adaptive estimating the value of a linear functional from indirect white noise observations. For a flexible approach, the problem is embedded in an abstract Hilbert scale. WeExpand
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Discretization strategy for linear ill-posed problems in variable Hilbert scales
The authors study the regularization of projection methods for solving linear ill-posed problems with compact and injective linear operators in Hilbert spaces. The smoothness of the unknown solutionExpand
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On adaptive inverse estimation of linear functionals in Hilbert scales
We address the problem of estimating the value of a linear functional h f , xi from random noisy observations of y 1⁄4 Ax in Hilbert scales. Both the white noise and density observation models areExpand
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Regularization Theory for Ill-Posed Problems: Selected Topics
TLDR
This monograph is a valuable contribution to the highly topical and extremely productive field of regularisation methods for inverse and ill-posed problems. Expand
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Morozov's discrepancy principle for tikhonov
In this paper severely ill-posed problems are studied which are represented in the form of linear operator equations with infinitely smoothing operators but with solutions having only a finiteExpand
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Regularization in Hilbert scales under general smoothing conditions
For solving linear ill-posed problems regularization methods are required when the available data include some noise. In the present paper regularized approximations are obtained by a generalExpand
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A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
The quasi-reversibility method of solving the Cauchy problem for the Laplace equation in a bounded domain ? is considered. With the help of the Carleman estimation technique improved error andExpand
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Balancing principle in supervised learning for a general regularization scheme
Abstract We discuss the problem of parameter choice in learning algorithms generated by a general regularization scheme. Such a scheme covers well-known algorithms as regularized least squares andExpand
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Discretization strategy for ill-posed problems in variable Hilbert scales
The authors study the regularization of projection methods for solving linear ill-posed problems with compact and injective linear operators in Hilbert spaces. Smoothness of the unknown solution isExpand
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