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SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 5, pp. 2773 - 2796
With given Fourier coefficients the evaluation of multivariate trigonometric polynomials at the nodes of a rank-1 lattice leads to a one-dimensional discrete... 
Hyperbolic cross | Lattice rule | Trigonometric approximation | Fast Fourier transform | MATHEMATICS, APPLIED | trigonometric approximation | hyperbolic cross | FOURIER-TRANSFORM | SPARSE GRIDS | ERROR | fast Fourier transform | lattice rule
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 11/2018, Volume 235, Issue 1, pp. 35 - 45
We have obtained the exact-by-order estimates of Kolmogorov, linear, and trigonometric widths of the classes Bp,θΩ $$ {B}_{p,\theta}^{\varOmega } $$ of... 
linear width | best approximation | Mathematics, general | trigonometric width | Mathematics | Kolmogorov width | graduated hyperbolic cross
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 5/2017, Volume 222, Issue 6, pp. 750 - 761
The order estimates of the best M-term trigonometric approximations of functions D β ψ $$ {D}_{\beta}^{\psi } $$ and the classes of (ψ , β)-differentiable... 
The best trigonometric approximation | Bernoulli kernel | Mathematics, general | Mathematics | Fourier series | stepwise hyperbolic cross | de la Vallée–Poissin kernel
Journal Article
Journal of Complexity, ISSN 0885-064X, 08/2015, Volume 31, Issue 4, pp. 543 - 576
In this paper, we present algorithms for the approximation of multivariate periodic functions by trigonometric polynomials. The approximation is based on... 
Hyperbolic cross | Trigonometric polynomials | Lattice rule | Taylor approximation | Approximation of multivariate functions | Fast Fourier transform | MATHEMATICS, APPLIED | SPACES | STABILITY | INTERPOLATION | MATHEMATICS | FOURIER-TRANSFORM | SPARSE GRIDS | Analysis | Algorithms
Journal Article
Journal of Complexity, ISSN 0885-064X, 06/2015, Volume 31, Issue 3, pp. 424 - 456
In this paper, we present error estimates for the approximation of multivariate periodic functions in periodic Hilbert spaces of isotropic and dominating mixed... 
Hyperbolic cross | Trigonometric polynomials | Lattice rule | Rank-1 lattice | Approximation of multivariate functions | Fast Fourier transform | INTERPOLATION | MATHEMATICS | MATHEMATICS, APPLIED | FOURIER-TRANSFORM | SPACES | SPARSE GRIDS
Journal Article
Journal of Complexity, ISSN 0885-064X, 10/2016, Volume 36, pp. 166 - 181
Journal Article
Numerical Algorithms, ISSN 1017-1398, 4/2006, Volume 41, Issue 4, pp. 339 - 352
Journal Article
Journal of Mathematical Sciences, ISSN 1072-3374, 11/2019, Volume 242, Issue 6, pp. 820 - 832
We obtained the exact-by-order estimates of some approximate characteristics of classes of the Nikol’skii–Besov type of periodic functions of one variable and... 
Mathematics, general | Mathematics | Classes of the Nikol’skii–Besov type | graduated hyperbolic cross | best orthogonal trigonometric approximation
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 10/2019, Volume 246, pp. 1 - 27
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize... 
Trigonometric polynomials | Lattice rule | Generalized hyperbolic cross | Fast Fourier transform | Approximation of multivariate periodic functions | Multiple rank-1 lattice | Generalized mixed smoothness | MATHEMATICS | ALGORITHMS | Algorithms
Journal Article
Scientific World Journal, ISSN 2356-6140, 2018, Volume 2018, pp. 1260325 - 17
A novel autonomous 5-D hyperjerk RC circuit with hyperbolic sine function is proposed in this paper. Compared to some existing 5-D systems like the 5-D Sprott... 
Computer simulation | Circuits | RC circuits | Bifurcations | Fractals | Semiconductor diodes | Hyperbolic functions | Dynamical systems | Physics | Investigations | Numerical analysis | Chaos theory | Organic light emitting diodes | Behavior | Trigonometric functions
Journal Article
Mathematical Notes, ISSN 0001-4346, 4/2010, Volume 87, Issue 3, pp. 403 - 415
We obtain order-sharp estimates of best approximations to the classes $B_{p,\theta }^r$ of periodic functions of several variables in the space L q , 1 ≤ p, q... 
Vallée-Poussin kernel | Fejér kernel | Fourier hyperbolic sum | hyperbolic cross | Bernoulli kernel | Mathematics, general | Mathematics | trigonometric polynomial | class $B_{p,\theta }^r$ of periodic functions
Journal Article
Mathematical Notes, ISSN 0001-4346, 7/2006, Volume 80, Issue 1, pp. 91 - 100
We obtain Bernstein and Jackson-Nikol’skii inequalities for trigonometric polynomials with spectrum generated by the level surfaces of a function Λ(t), and... 
Dirichlet kernel | Bernstein-type inequality | hyperbolic cross | Jackson-Nikol’skii inequality | spectrum of a polynomial | Mathematics, general | Mathematics | trigonometric polynomial
Journal Article
MATHEMATICAL NOTES, ISSN 0001-4346, 04/2010, Volume 87, Issue 3-4, pp. 403 - 415
We obtain order-sharp estimates of best approximations to the classes B-p(r),(theta) of periodic functions of several variables in the space L-q , 1 <= p, q <=... 
MATHEMATICS | Fourier hyperbolic sum | hyperbolic cross | Vallee-Poussin kernel | Bernoulli kernel | Fejer kernel | trigonometric polynomial | class B-p(,theta)r of periodic functions
Journal Article
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