4 citations · 4 across the 8 of their papers we have counts for
8 papers
Tractability versus curse of dimensionality for geometric -discrepancies
Erich Novak, Friedrich Pillichshammer
This paper studies tractability versus the curse of dimensionality for several geometric -discrepancies through a unified discrepancy--integration duality framework, where wor…
Extreme discrepancy, numerical integration and the curse of dimensionality
Erich Novak, Friedrich Pillichshammer
The classical notion of extreme discrepancy is a quantitative measure for the irregularity of distribution of finite point sets in the -dimensinal unit cube. In this paper…
Generalized Discrepancy of Random Points
Erich Novak, Friedrich Pillichshammer
We study the -discrepancy of random point sets in high dimensions, with emphasis on small values of . Although the classical -discrepancy suffers from the curse of dim…
Conditions for tractability of the weighted -discrepancy and integration in non-homogeneous tensor product spaces
Erich Novak, Friedrich Pillichshammer
We study tractability properties of the weighted -discrepancy. The concept of {\it weighted} discrepancy was introduced by Sloan and Woź\-nia\-kowski in 1998 in order to prove…
Intractability results for integration in tensor product spaces
Erich Novak, Friedrich Pillichshammer
We study lower bounds on the worst-case error of numerical integration in tensor product spaces. As reference we use the -th minimal error of linear rules that use function…
The -discrepancy for finite suffers from the curse of dimensionality
Erich Novak, Friedrich Pillichshammer
The -discrepancy is a classical quantitative measure for the irregularity of distribution of an -element point set in the -dimensional unit cube. Its inverse for dimensi…
Randomized approximation of summable sequences -- adaptive and non-adaptive
Robert Kunsch, Erich Novak, Marcin Wnuk
We prove lower bounds for the randomized approximation of the embedding based on algorithms that use arbitrary linear (hence non-adaptive) info…
The curse of dimensionality for the -discrepancy with finite
Erich Novak, Friedrich Pillichshammer
The -discrepancy is a quantitative measure for the irregularity of distribution of an -element point set in the -dimensional unit cube, which is closely related to the w…