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Applied Mathematical Sciences, ISSN 1312-885X, 2016, Volume 10, Issue 1-4, pp. 167 - 173
Journal Article
Journal of Complexity, ISSN 0885-064X, 12/2017, Volume 43, pp. 76 - 102
Many authors have studied exponentially-convergent tractability (EC-tractability) in the worst case setting. Here, we study EC-tractability in the average case... 
Tractability | Korobov kernel | Linear problem | Eigenvalue | Average case setting | EC-tractability | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | INTEGRATION
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 01/2020, Volume 249, p. 105309
This study aims at investigating Lp-approximation with 1≤p≤∞ defined over weighted Korobov spaces. The considered algorithms use finitely many evaluations of... 
Korobov kernel | Worst case setting | [formula omitted]-approximation | EC-tractability
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2016, Volume 34, pp. 42 - 49
In this paper we study d-variate approximation for weighted Korobov spaces in the worst-case setting. The considered algorithms use finitely many evaluations... 
Tractability | Korobov kernel | Linear problem | Eigenvalue | Worst case setting | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRATION | Matching | Algorithms | Approximation | Functionals | Mathematical analysis | Paper | Complexity
Journal Article
Advances in Difference Equations, ISSN 1687-1847, 12/2015, Volume 2015, Issue 1, pp. 1 - 13
Journal Article
Journal of Complexity, ISSN 0885-064X, 12/2019, Volume 55, p. 101412
This paper is devoted to discussing multivariate approximation problems with analytic Korobov kernels in the worst and average case settings. We consider... 
Analytic Korobov kernels | Exponential convergence tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | INTEGRATION | NUMBERS | LINEAR-PROBLEMS | AVERAGE-CASE TRACTABILITY | ENTROPY
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 301 - 338
We study multivariate approximation defined over tensor product Hilbert spaces. The space is a weighted tensor product Hilbert space with exponential weights... 
Tractability | Multivariate approximation | Hilbert spaces with exponential weights | KOROBOV SPACES | MATHEMATICS | INTEGRATION
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2019, Volume 52, pp. 24 - 44
We study approximation properties of centred additive random fields Yd, d∈N. The average case approximation complexity nYd(ε) is defined as the minimal number... 
Additive random fields | Korobov kernels | Asymptotic analysis | Average case approximation complexity | MATHEMATICS | MATHEMATICS, APPLIED | ALGORITHMS | Stochastic processes | Analysis
Journal Article
Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 03/2018, Volume 58, Issue 1, pp. 89 - 104
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2017, Volume 40, pp. 1 - 16
We introduce a new notion of tractability for multivariate problems, namely (s,lnκ)-weak tractability for positive s and κ. This allows us to study the... 
Tractability | Multivariate problem | Complexity | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | MULTIVARIATE INTEGRATION | Computer science
Journal Article
Journal of Complexity, ISSN 0885-064X, 08/2017, Volume 41, pp. 102 - 125
We study multivariate L∞-approximation for a weighted Korobov space of periodic functions for which the Fourier coefficients decay exponentially fast. The... 
Tractability | Exponential convergence | Worst-case error | Korobov spaces | Multivariate [formula omitted]-approximation | approximation | Multivariate L | Algorithms
Journal Article
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ISSN 0377-0427, 05/2017, Volume 315, pp. 327 - 342
In this paper we analyze the approximation of multivariate integrals over the Euclidean space for functions which are analytic. We show explicit upper bounds... 
KOROBOV SPACES | Exponential convergence | MATHEMATICS, APPLIED | Multiple integration | Error analysis | Trapezoidal rule | Euclidean space | FORMULA | Anisotropy | Analysis
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 98 - 126
We consider L2-approximation of elements of a Hermite space of analytic functions over Rs. The Hermite space is a weighted reproducing kernel Hilbert space of... 
Tractability | Hermite spaces | Exponential convergence | Multivariate approximation | MATHEMATICS | WEIGHTED KOROBOV SPACES | MULTIVARIATE INTEGRATION | Algorithms
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 04/2019, Volume 240, pp. 96 - 113
We analyze a new random algorithm for numerical integration of d-variate functions over [0,1]d from a weighted Sobolev space with dominating mixed smoothness... 
Tractability | Randomized algorithms | Numerical integration | Lattice rules | MATHEMATICS | WEIGHTED KOROBOV | ALGORITHMS | BY-COMPONENT CONSTRUCTION | MULTIVARIATE INTEGRATION | MONTE | Computer science | Analysis | Algorithms
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2018, Volume 46, pp. 103 - 112
In this paper we study tractability properties of the weighted star discrepancy with general coefficients of centered regular grids with different mesh-sizes.... 
Tractability | Quasi-Monte Carlo | Weighted star discrepancy | Regular grid | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | ALGORITHMS | MULTIVARIATE INTEGRATION
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2017, Volume 208, Issue 1, pp. 60 - 74
In this paper, we study Korobov polynomials of the first kind from the viewpoint of umbral calculus and give new identities for them, associated with special... 
Umbral calculus | Korobov polynomials of the first kind | MATHEMATICS | umbral calculus | Polynomials | Mathematical analysis | Calculus
Journal Article
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