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Approximation Complexity of Additive Random Fields

Abstract : Let X (t), t ∈ [0, 1]d be an additive random field. We investigate the complexity of finite rank approximation n X (t, ω) ≈ ) ξk (ω)ϕk (t). k=1 The results obtained in asymptotic setting d → ∞, as suggested H.Wo'zniakowski, provide quantitative version of dimension curse phe- nomenon: we show that the number of terms in the series needed to obtain a given relative approximation error depends on d exponentially and find the explosion coefficients.
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Mihail A. Lifshits, Marguerite Zani. Approximation Complexity of Additive Random Fields. Journal of Complexity, Elsevier, 2008, 24 (3), pp.362--379. ⟨hal-00796311⟩

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