Asymptotic analysis in multivariate worst case approximation with Gaussian kernels

06/25/2023

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We consider a problem of approximation of d-variate functions defined on ℝ^d 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→∞.

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