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SIAM REVIEW, ISSN 0036-1445, 09/2019, Volume 61, Issue 3, pp. 443 - 473
Functions of one or more variables are usually approximated with a basis: a complete, linearly independent system of functions that spans a suitable function... 
RIESZ BASIS | MATHEMATICS, APPLIED | SMOOTH FUNCTIONS | RECOVERING EXPONENTIAL ACCURACY | frames | ill-conditioning | FOURIER EXTENSIONS | FINITE SECTION METHOD | ALGORITHMS | OPERATOR | function approximation | SPHEROIDAL WAVE-FUNCTIONS | TIGHT FRAMES | UNCERTAINTY | singular value decomposition
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 11/2018, Volume 275, Issue 9, pp. 2538 - 2571
We prove the density of smooth functions in the modular topology in Musielak–Orlicz–Sobolev spaces essentially extending the results of Gossez [17] obtained in... 
The Musielak–Orlicz–Sobolev spaces | Density of smooth functions | The Lavrentiev phenomenon | RENORMALIZED SOLUTIONS | FLUIDS | MATHEMATICS | REGULARITY | The Musielak-Orlicz-Sobolev spaces | GROWTH | FUNCTIONALS | Mathematics - Functional Analysis
Journal Article
Mechanism and Machine Theory, ISSN 0094-114X, 05/2014, Volume 75, pp. 1 - 11
The paper deals with the research of sigmoid smooth curve application to the approximation of GMS (Generalized Maxwell-Slip) friction model. The study provides... 
Sigmoid function | Modelling | Simulation | Smooth function | Dry friction | COMPENSATION | BEHAVIOR | LUGRE | DIFFERENTIAL-EQUATIONS | MATLAB | ENGINEERING, MECHANICAL | SLIDING FRICTION | HYSTERESIS | SYSTEMS | Approximation | Friction | Lyapunov exponents | Dynamics | Mathematical analysis | Differential equations | Mathematical models | Dynamical systems
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2019, Volume 469, Issue 2, pp. 661 - 704
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 05/2019, Volume 276, Issue 10, pp. 3226 - 3260
Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on c0(Γ) can be approximated uniformly on bounded sets by polyhedral... 
Renorming | Polyhedrality | Approximation | Smoothness | MATHEMATICS | POLYHEDRAL APPROXIMATION | SMOOTH APPROXIMATIONS
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 885 - 905
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2007, Volume 29, Issue 2, pp. 434 - 454
For the low-rank approximation of time-dependent data matrices and of solutions to matrix differential equations, an increment-based computational approach is... 
Matrix differential equations | Time-varying matrices | Smooth decomposition | Low-rank approximation | Continuous updating | MATRIX | MATHEMATICS, APPLIED | continuous updating | SINGULAR-VALUE DECOMPOSITION | time-varying matrices | matrix differential equations | smooth decomposition | low-rank approximation
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 526 - 538
This article is devoted to smooth approximation of convex functions on Banach spaces with smooth norm. We prove that if X⁎ is a smooth space and f is a... 
Convex function | Gâteaux differentiable | Smooth space | Uniform approximation | MATHEMATICS | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | DIFFERENTIABILITY | Gateaux differentiable
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 259, Issue 3, pp. 561 - 582
We prove, among other things, that a Lipschitz (or uniformly continuous) mapping f : X → Y can be approximated (even in a fine topology) by smooth Lipschitz... 
Smoothness | Lipschitz | Approximation | MATHEMATICS | BANACH-SPACES | C-P-SMOOTH
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 06/2015, Volume 216, Issue 3, pp. 813 - 879
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 09/2017, Volume 43, Issue 2, pp. 292 - 316
Spherical needlets are highly localized radial polynomials on the sphere S ⊂R , d≥2, with centers at the nodes of a suitable cubature rule. The original... 
Sphere | Wavelet | Frame | Spherical design | Needlet | Filtered hyperinterpolation | Localization | MATHEMATICS, APPLIED | SMOOTH FUNCTIONS | SPACES | PHYSICS, MATHEMATICAL | DESIGNS | FRAMES | ERROR
Journal Article
Neural Networks, ISSN 0893-6080, 10/2017, Volume 94, pp. 103 - 114
We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for... 
Approximation complexity | Deep ReLU networks | NEURAL-NETWORKS | DIMENSION | SMOOTH | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Neural Networks (Computer) | Neural networks
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/2019, Volume 60, Issue 10, p. 102103
We study the convergence in L2 of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the... 
SPACE | SMOOTH FUNCTIONAL-DERIVATIVES | EQUATIONS | CONVERGENCE | MULTIPLIERS | POWER-SERIES EXPANSION | TERM | PHYSICS, MATHEMATICAL | Organic chemistry | Time-frequency analysis | Approximation | Function space | Mathematical analysis | Integrals | Series expansion | Frequency analysis | Slicing
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 324 - 337
In this paper, we consider the smooth solutions to the Cauchy problem for the diffusion approximation radiation hydrodynamics equations in R3. The model... 
Diffusion approximation | Radiation hydrodynamics | Smooth solutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MODEL
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 348 - 379
We prove sharp, two-sided bounds on sums of the form ∑k∈N0d∖Da(T)exp(−∑j=1dajkj), where Da(T):={k∈N0d:∑j=1dajkj≤T} and a∈R+d. These sums appear in the error... 
Interpolation | Sparse grids | Integration | Multivariate approximation | Analytic functions | Infinite dimensions | SMOOTH FUNCTIONS | SPACES | EQUATIONS | STOCHASTIC COLLOCATION | MATHEMATICS | BOUNDS | CONVERGENCE
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 2, pp. 1262 - 1272
We show that norms on certain Banach spaces X can be approximated uniformly, and with arbitrary precision, on bounded subsets of X by C∞ smooth norms and... 
Renorming | James boundary | Polyhedral norm | Smooth norm | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARIES | CONVEX-BODIES | NORMS
Journal Article
Neurocomputing, ISSN 0925-2312, 01/2016, Volume 175, pp. 348 - 354
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 05/2017, Volume 154, pp. 258 - 268
The first goal of this paper is to give a short description of the planar bi-Sobolev homeomorphisms, providing simple and self-contained proofs for some... 
Bi-Sobolev homeomorphisms | Smooth approximation | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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