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Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803

- P. Mathé, S. Pereverzev
- Mathematics
- 1 June 2003

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 general… Expand

251 24- PDF

Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations

- A. Goldenshluger, S. Pereverzev
- Mathematics
- 1 October 2000

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. We… Expand

77 6- PDF

Discretization strategy for linear ill-posed problems in variable Hilbert scales

- P. Mathé, S. Pereverzev
- Mathematics
- 17 October 2003

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 solution… Expand

84 6

On adaptive inverse estimation of linear functionals in Hilbert scales

- A. Goldenshluger, S. Pereverzev
- Mathematics
- 1 October 2003

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 are… Expand

37 6- PDF

Regularization Theory for Ill-Posed Problems: Selected Topics

- Shuai Lu, S. Pereverzev
- Computer Science
- 17 July 2013

TLDR

66 5

Morozov's discrepancy principle for tikhonov

- S. Pereverzev, E. Schock
- Mathematics
- 1 January 2000

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 finite… Expand

49 4

Regularization in Hilbert scales under general smoothing conditions

- M. T. Nair, S. Pereverzev, U. Tautenhahn
- Mathematics
- 1 December 2005

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 general… Expand

88 4- PDF

A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation

- Hui Cao, M. Klibanov, S. Pereverzev
- Mathematics
- 1 March 2009

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 and… Expand

61 4

Balancing principle in supervised learning for a general regularization scheme

- Shuai Lu, P. Mathé, S. Pereverzev
- Mathematics
- 2020

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 and… Expand

16 3- PDF

Discretization strategy for ill-posed problems in variable Hilbert scales

- P. Mathé, S. Pereverzev
- 2003

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 is… Expand

7 3- PDF

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