Very Low Truncation Dimension for High Dimensional Integration Under Modest Error Demand

2015/06/08 by Kritzer, P., Pillichshammer, F., Wasilkowski, G. W.
#65D30 #65D32 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1506.02458

Abstract

We consider the problem of numerical integration for weighted anchored and ANOVA Sobolev spaces of s-variate functions. Here s is large including s=∞. Under the assumption of sufficiently fast decaying weights, we prove in a constructive way that such integrals can be approximated by quadratures for functions f_k with only k variables, where k=k(ε) depends solely on the error demand ε and is surprisingly small when s is sufficiently large relative to ε. This holds, in particular, for s=∞ and arbitrary ε since then k(ε)

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