The Gel'fand Approximations on Multivariate Functions in the Deterministic and Monte Carlo Settings

Jing Fan Long; Li Qin Duan; Pei Xin Ye

doi:10.4028/www.scientific.net/AMM.543-547.1609

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 543-547The Gel'fand Approximations on Multivariate...

The Gel'fand Approximations on Multivariate Functions in the Deterministic and Monte Carlo Settings

Abstract:

The concept of Gel'fand width plays an important role in the theory of information complexity and compressed sensing. In this paper, we study the approximation problems on the generalized Besov classesB^Ω_Ρ,θ in the norm of Lq by the Gel'fand methods in the deterministic and the Monte Carlo settings. Applying the Maiorov's discretization technique and some properties of pseudo-s-scale, we determine the asymptotic orders of this problem for some values of parameters p, q, θ.

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Applied Mechanics and Materials (Volumes 543-547)

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1609-1612

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.543-547.1609

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Online since:

March 2014

Authors:

Jing Fan Long*, Li Qin Duan, Pei Xin Ye

Keywords:

Asymptotic Order, Gelfand Approximation, Generalized Besov Class, Width

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