Asymptotic analysis in multivariate worst case approximation with Gaussian kernels

We consider a problem of approximation of d-variate functions defined on Rd which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we investigate the growth of the information complexity as d→∞. The asymptotics...

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Bibliographic Details
Published in:	Journal of Complexity Vol. 82; p. 101838
Main Authors:	Khartov, A.A., Limar, I.A.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-06-2024
Subjects:	Asymptotic analysis Gaussian kernels Information-based complexity Multivariate approximation problems Tractability Worst case setting Tractability 41A25 Information-based complexity 41A63 41A65 65J10 Worst case setting 65Y20 Gaussian kernels Multivariate approximation problems Asymptotic analysis
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Summary:	We consider a problem of approximation of d-variate functions defined on Rd which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we investigate the growth of the information complexity as d→∞. The asymptotics are obtained for the case of fixed error threshold and for the case when it goes to zero as d→∞.
ISSN:	0885-064X 1090-2708
DOI:	10.1016/j.jco.2024.101838