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Estimates of probabilistic widths of the diagonal operator of finite-dimensional sets with the Gaussian measure
In this paper, we estimate the asymptotic orders of probabilistic and average widths of the compact embedding operators from the Sobolev space
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Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method
The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison...
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Approximation by neural networks with sigmoidal functions
In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the...
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Bernstein n-widths of Besov embeddings on Lipschitz domains
In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov,...
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Existence of the best n-term approximants for structured dictionaries
This paper investigates the existence of elements of the best n -term approximation in infinite dimensional Hilbert spaces. The notion of uniform...
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Bernstein Widths and Super Strictly Singular Inclusions
The super strict singularity of inclusions between rearrangement invariant function spaces on [0, 1] is studied. Estimates of the Bernstein widths...
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Entropy Numbers of Quadratic Forms and Their Applications to Spectral Theory
We estimate the entropy numbers of related compact embeddings and apply the outcome to say something about the distribution of eigenvalues of the...
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Super greedy type algorithms
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard...
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On manifolds of tensors of fixed TT-rank
Recently, the format of TT tensors (Hackbusch and Kühn in J Fourier Anal Appl 15:706–722,
2009 ; Oseledets in SIAM J Sci Comput2009 , submitted;... -
An optimal multivariate spline method of recovery of twice differentiable functions
A continuous quadratic polynomial spline of several variables is constructed. It solves the optimal recovery problem studied by V.F. Babenko, S.V....
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Error Estimates for Orthogonal Matching Pursuit and Random Dictionaries
In this paper we investigate the efficiency of the Orthogonal Matching Pursuit algorithm (OMP) for random dictionaries. We concentrate on...
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Regularity of Tensor Product Approximations to Square Integrable Functions
We investigate first-order conditions for canonical and optimal subspace (Tucker format) tensor product approximations to square integrable...
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Eigenvalue distributions of some non-isotropic degenerate elliptic operators
The paper deals with the distribution of eigenvalues of some degenerate elliptic operators in the unit square defined via closable symmetric singular...
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Greedy approximation with regard to non-greedy bases
The main goal of this paper is to understand which properties of a basis are important for certain direct and inverse theorems in nonlinear...
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An Asymptotic Sampling Recomposition Theorem for Gaussian Signals
For any Gaussian signal and every given sampling frequency we prove an asymptotic property of type Shannon’s sampling theorem, based on normalized...
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Entropy numbers in function spaces with mixed integrability
This paper deals with entropy numbers for compact embeddings of Besov-Sobolev spaces with mixed integrability into Lebesgue spaces.
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Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations
Problems of best tensor product approximation of low orthogonal rank can be formulated as maximization problems on Stiefel manifolds. The functionals...