Asymptotic analysis of average case approximation complexity of additive random fields

2017/10/30 by A. A. Khartov, Khartov, A. A., Marguerite Zani +2
Mathematics · #Applied mathematics #Approximation error #Combinatorics #Discrete mathematics #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1710.10865

arxiv created 2017/10/30 · openalex publication_date 2017/10/30 · arxiv updated 2017/10/31 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

We study approximation properties of sequences of centered additive random fields Y_d, d∈ℕ. The average case approximation complexity n^Y_d(ε) is defined as the minimal number of evaluations of arbitrary linear functionals that is needed to approximate Y_d with relative 2-average error not exceeding a given threshold ε∈(0,1). We investigate the growth of n^Y_d(ε) for arbitrary fixed ε∈(0,1) and d→∞. Under natural assumptions we obtain general results concerning asymptotics of n^Y_d(ε). We apply our results to additive random fields with marginal random processes corresponding to the Korobov kernels.

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