The Experts below are selected from a list of 40125 Experts worldwide ranked by ideXlab platform
Gianluca Vinti - One of the best experts on this subject based on the ideXlab platform.
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pointwise and Uniform Approximation by multivariate neural network operators of the max product type
Neural Networks, 2016Co-Authors: Danilo Costarelli, Gianluca VintiAbstract:In this article, the theory of multivariate max-product neural network (NN) and quasi-interpolation operators has been introduced. Pointwise and Uniform Approximation results have been proved, together with estimates concerning the rate of convergence. At the end, several examples of sigmoidal activation functions have been provided.
Danilo Costarelli - One of the best experts on this subject based on the ideXlab platform.
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pointwise and Uniform Approximation by multivariate neural network operators of the max product type
Neural Networks, 2016Co-Authors: Danilo Costarelli, Gianluca VintiAbstract:In this article, the theory of multivariate max-product neural network (NN) and quasi-interpolation operators has been introduced. Pointwise and Uniform Approximation results have been proved, together with estimates concerning the rate of convergence. At the end, several examples of sigmoidal activation functions have been provided.
M A Komarov - One of the best experts on this subject based on the ideXlab platform.
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a criterion for the best Uniform Approximation by simple partial fractions in terms of alternance
Izvestiya: Mathematics, 2015Co-Authors: M A KomarovAbstract:In the problem of approximating real functions by simple partial fractions of order on closed intervals , we obtain a criterion for the best Uniform Approximation which is similar to Chebyshev's alternance theorem and considerably generalizes previous results: under the same condition on the poles of the fraction of best Approximation, we omit the restriction on the order of this fraction. In the case of Approximation of odd functions on , we obtain a similar criterion under much weaker restrictions on the position of the poles : the disc is replaced by the domain bounded by a lemniscate contained in this disc. We give some applications of this result. The main theorems are extended to the case of weighted Approximation. We give a lower bound for the distance from to the set of poles of all simple partial fractions of order which are normalized with weight on (a weighted analogue of Gorin's problem on the semi-axis).
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an example of non uniqueness of a simple partial fraction of the best Uniform Approximation
Russian Mathematics, 2013Co-Authors: M A KomarovAbstract:For arbitrary natural n ≥ 2 we construct an example of a real continuous function, for which there exists more than one simple partial fraction of order ≤ n of the best Uniform Approximation on a segment of the real axis. We prove that even the Chebyshev alternance consisting of n+1 points does not guarantee the uniqueness of the best Approximation fraction. The obtained results are generalizations of known non-uniqueness examples constructed for n = 2, 3 in the case of simple partial fractions of an arbitrary order n.
Abderrazek Karoui - One of the best experts on this subject based on the ideXlab platform.
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Uniform Approximation and Explicit Estimates for the Prolate Spheroidal Wave Functions
Constructive Approximation, 2016Co-Authors: Aline Bonami, Abderrazek KarouiAbstract:For fixed c , prolate spheroidal wave functions (PSWFs), denoted by $$\psi _{n, c}$$ ψ n , c , form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith c . They have been widely studied and used after the seminal work of D. Slepian and his co-authors. In several applications, Uniform estimates of the $$\psi _{n,c}$$ ψ n , c in n and c are needed. To progress in this direction, we push forward the Uniform Approximation error bounds and give an explicit Approximation of their values at 1 in terms of the Legendre complete elliptic integral of the first kind. Also, we give an explicit formula for the accurate Approximation of the eigenvalues of the Sturm–Liouville operator associated with the PSWFs.
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Uniform Approximation and Explicit Estimates for the Prolate Spheroidal Wave Functions
Constructive Approximation, 2015Co-Authors: Aline Bonami, Abderrazek KarouiAbstract:For xed c, Prolate Spheroidal Wave Functions (PSWFs), denoted by ψ n,c , form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith c. They have been largely studied and used after the seminal work of D. Slepian and his co-authors. In several applications, Uniform estimates of the ψ n,c in n and c, are needed. To progress in this direction, we push forward the Uniform Approximation error bounds and give an explicit Approximation of their values at 1 in terms of the Legendre complete elliptic integral of the rst kind. Also, we give an explicit formula for the accurate Approximation the eigenvalues of the Sturm-Liouville operator associated with the PSWFs. 2010 Mathematics Subject Classication. Primary 42C10, 65L70. Secondary 41A60, 65L15.
W Becker - One of the best experts on this subject based on the ideXlab platform.
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high order above threshold ionization the Uniform Approximation and the effect of the binding potential
Physical Review A, 2002Co-Authors: Figueira C De Morisson Faria, Henning Schomerus, W BeckerAbstract:A versatile semiclassical Approximation for intense laser-atom processes is presented. This Uniform Approximation is no more complicated than the frequently used multidimensional saddle-point Approximation and far superior, since it applies for all energies, both close to as well as away from the classical cutoffs. In the latter case, it reduces to the standard saddle-point Approximation. The Uniform Approximation agrees accurately with numerical evaluations for potentials, for which these are feasible, and constitutes a practicable method of calculation, in general. The method is applied to the calculation of high-order above-threshold ionization spectra with various binding potentials: Coulomb, Yukawa, and shell potentials which may model C60 molecules or clusters. The shell potentials generate rescattering spectra that are more structured and may feature an apparently higher cutoff.
