Truncation Dimension for Function Approximation

2016/10/10 by Kritzer, Peter, Pillichshammer, Friedrich, Wasilkowski, G. W.
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1610.02852

Abstract

We consider approximation of functions of s variables, where s is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very small number \rm dim^trnc(ε) of variables. Here ε is the error demand and we refer to \rm dim^trnc(ε) as the ε-truncation dimension. We show that for sufficiently fast decaying product weights and modest error demand (up to about ε ≈ 10^-5) the truncation dimension is surprisingly very small.

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