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- W2980197566 abstract "The purpose of this paper is to extend the result of arXiv:1810.00823 to mixed Holder functions on $[0,1]^d$ for all $d ge 1$. In particular, we prove that by sampling an $alpha$-mixed Holder function $f : [0,1]^d rightarrow mathbb{R}$ at $sim frac{1}{varepsilon} left(log frac{1}{varepsilon} right)^d$ independent uniformly random points from $[0,1]^d$, we can construct an approximation $tilde{f}$ such that $$ |f - tilde{f}|_{L^2} lesssim varepsilon^alpha left(log textstyle{frac{1}{varepsilon}} right)^{d-1/2}, $$ with high probability." @default.
- W2980197566 created "2019-10-18" @default.
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- W2980197566 date "2019-10-09" @default.
- W2980197566 modified "2023-09-27" @default.
- W2980197566 title "Randomized mixed Hölder function approximation in higher-dimensions" @default.
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