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- W1586769266 abstract "The star discrepancy is a measure of how uniformly distributed a finite point set is in the d-dimensional unit cube. It is related to high-dimensional numerical integration of certain function classes as expressed by the Koksma-Hlawka inequality. A sharp version of this inequality states that the worst-case error of approximating the integral of functions from the unit ball of some Sobolev space by an equal-weight cubature is exactly the star discrepancy of the set of sample points. In many applications, as, e.g., in physics, quantum chemistry or finance, it is essential to approximate high-dimensional integrals. Thus with regard to the Koksma-Hlawka inequality the following three questions are very important: We want to discuss these questions and survey and explain some approaches to tackle them relying on metric entropy, randomization, and derandomization." @default.
- W1586769266 created "2016-06-24" @default.
- W1586769266 creator A5027293444 @default.
- W1586769266 date "2012-01-01" @default.
- W1586769266 modified "2023-09-25" @default.
- W1586769266 title "Entropy, Randomization, Derandomization, and Discrepancy" @default.
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- W1586769266 doi "https://doi.org/10.1007/978-3-642-27440-4_3" @default.
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