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

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

linear width | best approximation | Mathematics, general | trigonometric width | Mathematics | Kolmogorov width | graduated hyperbolic cross

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2010, Volume 47, Issue 6, pp. 4415 - 4428

A straightforward discretization of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even...

Interpolation | Approximation | Polynomials | Matrices | Fourier coefficients | Fast Fourier transformations | Toolboxes | Spatial dimensions | Arithmetic | Hyperbolic cross | Fast fourier transform | Sparse grid | Trigonometric approximation | Nonequispaced FFT | INTERPOLATION | MATHEMATICS, APPLIED | trigonometric approximation | DESIGN | nonequispaced FFT | TRIGONOMETRIC POLYNOMIALS | hyperbolic cross | SPARSE GRIDS | ALGORITHM | sparse grid | fast Fourier transform | Fourier transforms | Mathematical analysis | Fourier analysis | Mathematical models | Computational efficiency | Derivatives | Numerical Analysis | Mathematics

Interpolation | Approximation | Polynomials | Matrices | Fourier coefficients | Fast Fourier transformations | Toolboxes | Spatial dimensions | Arithmetic | Hyperbolic cross | Fast fourier transform | Sparse grid | Trigonometric approximation | Nonequispaced FFT | INTERPOLATION | MATHEMATICS, APPLIED | trigonometric approximation | DESIGN | nonequispaced FFT | TRIGONOMETRIC POLYNOMIALS | hyperbolic cross | SPARSE GRIDS | ALGORITHM | sparse grid | fast Fourier transform | Fourier transforms | Mathematical analysis | Fourier analysis | Mathematical models | Computational efficiency | Derivatives | Numerical Analysis | Mathematics

Journal Article

Journal of Mathematical Sciences (United States), ISSN 1072-3374, 05/2017, Volume 222, Issue 6, pp. 750 - 761

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

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

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

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

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2013, Volume 13, Issue 6, pp. 965 - 1003

In this paper, we study linear trigonometric hyperbolic cross approximations, Kolmogorov n-widths d n (W,H γ ), and ε-dimensions n ε (W,H γ ) of periodic...

Economics general | Sobolev space | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Kolmogorov n -widths | 41A25 | 41A63 | Numerical Analysis | Trigonometric hyperbolic cross space | 42A10 | High-dimensional approximation | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Function classes with anisotropic smoothness | ε -dimensions | MATHEMATICS, APPLIED | GRIDS | SPACES | ELECTRONIC SCHRODINGER-EQUATION | Kolmogorov n-widths | SPARSE FINITE-ELEMENTS | epsilon-dimensions | INTERPOLATION | MATHEMATICS | ELLIPTIC PROBLEMS | VARIABLES | COMPUTER SCIENCE, THEORY & METHODS | BOUNDED MIXED DERIVATIVES | ε-dimensions

Economics general | Sobolev space | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Kolmogorov n -widths | 41A25 | 41A63 | Numerical Analysis | Trigonometric hyperbolic cross space | 42A10 | High-dimensional approximation | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Function classes with anisotropic smoothness | ε -dimensions | MATHEMATICS, APPLIED | GRIDS | SPACES | ELECTRONIC SCHRODINGER-EQUATION | Kolmogorov n-widths | SPARSE FINITE-ELEMENTS | epsilon-dimensions | INTERPOLATION | MATHEMATICS | ELLIPTIC PROBLEMS | VARIABLES | COMPUTER SCIENCE, THEORY & METHODS | BOUNDED MIXED DERIVATIVES | ε-dimensions

Journal Article

Journal of Complexity, ISSN 0885-064X, 10/2016, Volume 36, pp. 166 - 181

We develop algorithms for multivariate integration and approximation in the weighted half-period cosine space of smooth non-periodic functions. We use...

Cosine series | Hyperbolic crosses | Quasi-Monte Carlo methods | Function approximation | Component-by-component construction | Rank-[formula omitted] lattice rules | Rank-1 lattice rules | MATHEMATICS, APPLIED | TRIGONOMETRIC POLYNOMIALS | ALGORITHMS | MATHEMATICS | ACHIEVE | CONVERGENCE | BY-COMPONENT CONSTRUCTION | Algorithms | Mathematics - Numerical Analysis

Cosine series | Hyperbolic crosses | Quasi-Monte Carlo methods | Function approximation | Component-by-component construction | Rank-[formula omitted] lattice rules | Rank-1 lattice rules | MATHEMATICS, APPLIED | TRIGONOMETRIC POLYNOMIALS | ALGORITHMS | MATHEMATICS | ACHIEVE | CONVERGENCE | BY-COMPONENT CONSTRUCTION | Algorithms | Mathematics - Numerical Analysis

Journal Article

Numerical Algorithms, ISSN 1017-1398, 4/2006, Volume 41, Issue 4, pp. 339 - 352

The discrete Fourier transform in d dimensions with equispaced knots in space and frequency domain can be computed by the fast Fourier transform (FFT) in...

trigonometric approximation | NFFT | 65T40 | Numeric Computing | fast Fourier transform for nonequispaced knots | Theory of Computation | sparse grids | Algorithms | Algebra | 65F10 | hyperbolic cross | FFT | Computer Science | Mathematics, general | 65F15 | Hyperbolic cross | Sparse grids | Fast Fourier transform for nonequispaced knots | Trigonometric approximation | MATHEMATICS, APPLIED | FAST FOURIER-TRANSFORMS

trigonometric approximation | NFFT | 65T40 | Numeric Computing | fast Fourier transform for nonequispaced knots | Theory of Computation | sparse grids | Algorithms | Algebra | 65F10 | hyperbolic cross | FFT | Computer Science | Mathematics, general | 65F15 | Hyperbolic cross | Sparse grids | Fast Fourier transform for nonequispaced knots | Trigonometric approximation | MATHEMATICS, APPLIED | FAST FOURIER-TRANSFORMS

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

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

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

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

Nonlinear Dynamics, ISSN 0924-090X, 7/2017, Volume 89, Issue 2, pp. 1047 - 1061

In this work, one of the most simple chaotic autonomous circuits, which has been reported in the literature, is presented. The proposed circuit, that belongs...

Chaos | Engineering | Vibration, Dynamical Systems, Control | NIST-800-22 | Random number generator | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Antimonotonicity | Sound encryption | Coexisting attractors | Nonlinear circuit | DESIGN | MULTI-SCROLL | PERFORMANCE | IMPLEMENTATION | ENGINEERING, MECHANICAL | SYNCHRONIZATION | ATTRACTORS | MECHANICS | NEURAL-NETWORKS | DYNAMICS | SYSTEMS | GENERATION | Random numbers | Data encryption | Circuits | Chaos theory | Organic light emitting diodes | Sound | Encryption | Hyperbolic functions | Trigonometric functions

Chaos | Engineering | Vibration, Dynamical Systems, Control | NIST-800-22 | Random number generator | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Antimonotonicity | Sound encryption | Coexisting attractors | Nonlinear circuit | DESIGN | MULTI-SCROLL | PERFORMANCE | IMPLEMENTATION | ENGINEERING, MECHANICAL | SYNCHRONIZATION | ATTRACTORS | MECHANICS | NEURAL-NETWORKS | DYNAMICS | SYSTEMS | GENERATION | Random numbers | Data encryption | Circuits | Chaos theory | Organic light emitting diodes | Sound | Encryption | Hyperbolic functions | Trigonometric functions

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2/2017, Volume 55, Issue 2, pp. 632 - 660

Although the HDMR decomposition has become an important tool for the understanding of high dimensional functions, the fundamental conjecture underlying its...

Theoretical and Computational Chemistry | Chemistry | HDMR fundamental conjecture | Physical Chemistry | High dimensional functions | Fourier-HDMR approximation | Multiple Fourier series | Domain decomposition | Math. Applications in Chemistry | CROSS TRIGONOMETRIC POLYNOMIALS | HYPERBOLIC CROSS | ANOVA DECOMPOSITION | DIMENSIONAL MODEL REPRESENTATIONS | CHEMISTRY, MULTIDISCIPLINARY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SENSITIVITY-ANALYSIS | EXPANSION | TRANSFORM | LATTICES | Fourier analysis | Models | Approximation theory | Analysis | Decomposition (Mathematics)

Theoretical and Computational Chemistry | Chemistry | HDMR fundamental conjecture | Physical Chemistry | High dimensional functions | Fourier-HDMR approximation | Multiple Fourier series | Domain decomposition | Math. Applications in Chemistry | CROSS TRIGONOMETRIC POLYNOMIALS | HYPERBOLIC CROSS | ANOVA DECOMPOSITION | DIMENSIONAL MODEL REPRESENTATIONS | CHEMISTRY, MULTIDISCIPLINARY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SENSITIVITY-ANALYSIS | EXPANSION | TRANSFORM | LATTICES | Fourier analysis | Models | Approximation theory | Analysis | Decomposition (Mathematics)

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

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

European Journal of Control, ISSN 0947-3580, 01/2019, Volume 45, pp. 30 - 44

This work targets the problem of leader following consensus in heterogeneous multi-agent systems described by second order nonlinear dynamics. The controller...

Event-triggered sliding modes | Inverse sine hyperbolic reaching law | Nonlinear gain | Event-triggered leader following Tracking control | Formation keeping | Heterogeneous second order multi-agent systems (MAS) | Inter event execution time | Consensus | STIRRED-TANK REACTOR | NETWORKS | AUTOMATION & CONTROL SYSTEMS | Control | Sliding mode control | Methods | Multi-agent systems | Controllers | Nonlinear dynamics | Multiagent systems | Costs | Computer simulation | Hyperbolic functions | Dynamical systems | Semantic web | Embedded systems | Simulation | Robustness (mathematics) | Computation | Control algorithms | Energy efficiency | Trigonometric functions | Nonlinear systems | Nonlinear control | Communication

Event-triggered sliding modes | Inverse sine hyperbolic reaching law | Nonlinear gain | Event-triggered leader following Tracking control | Formation keeping | Heterogeneous second order multi-agent systems (MAS) | Inter event execution time | Consensus | STIRRED-TANK REACTOR | NETWORKS | AUTOMATION & CONTROL SYSTEMS | Control | Sliding mode control | Methods | Multi-agent systems | Controllers | Nonlinear dynamics | Multiagent systems | Costs | Computer simulation | Hyperbolic functions | Dynamical systems | Semantic web | Embedded systems | Simulation | Robustness (mathematics) | Computation | Control algorithms | Energy efficiency | Trigonometric functions | Nonlinear systems | Nonlinear control | Communication

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

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

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

Remote Sensing, ISSN 2072-4292, 04/2018, Volume 10, Issue 4, p. 613

Transmission line corridor (i.e., Right-of-Ways (ROW)) clearance management plays a critically important role in power line risk management and is an important...

Feature Extraction | UAV | Power transmission lines inspection | Clearance anomaly | LiDAR | Point clouds | point clouds | INSPECTION | DISTANCE | SCANNING POINT CLOUDS | VEGETATION MANAGEMENT | CLASSIFICATION | MAPPING SYSTEM | HEIGHT | clearance anomaly | EXTRACTION | REMOTE SENSING | IMAGES | POWER-LINES | power transmission lines inspection | Feature maps | Differential geometry | Adaptive filters | Data transmission | Mathematics | Encroachment | Accuracy | Unmanned aerial vehicles | Mathematical models | Trigonometric functions | Automatic transmissions | Continuity (mathematics) | Trees | Euclidean geometry | Inspection | Hazards | Hyperbolic functions | Clustering | Pylons | Terrain | Lidar | Corridors | Distance measurement | Risk management | Three dimensional models | Power lines | Anomalies

Feature Extraction | UAV | Power transmission lines inspection | Clearance anomaly | LiDAR | Point clouds | point clouds | INSPECTION | DISTANCE | SCANNING POINT CLOUDS | VEGETATION MANAGEMENT | CLASSIFICATION | MAPPING SYSTEM | HEIGHT | clearance anomaly | EXTRACTION | REMOTE SENSING | IMAGES | POWER-LINES | power transmission lines inspection | Feature maps | Differential geometry | Adaptive filters | Data transmission | Mathematics | Encroachment | Accuracy | Unmanned aerial vehicles | Mathematical models | Trigonometric functions | Automatic transmissions | Continuity (mathematics) | Trees | Euclidean geometry | Inspection | Hazards | Hyperbolic functions | Clustering | Pylons | Terrain | Lidar | Corridors | Distance measurement | Risk management | Three dimensional models | Power lines | Anomalies

Journal Article

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