54 citations · 196 across the 25 of their papers we have counts for
27 papers
Exponential tractability of linear tensor product problems
Fred J. Hickernell, Peter Kritzer, Henryk Wozniakowski
In this article we consider the approximation of compact linear operators defined over tensor product Hilbert spaces. Necessary and sufficient conditions on the singular values of…
Notes on tractability conditions for linear multivariate problems
Peter Kritzer, Henryk Wozniakowski
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. The…
Tractability of multivariate problems for standard and linear information in the worst case setting: part II
Henryk Woźniakowski, Erich Novak
We study QPT (quasi-polynomial tractability) in the worst case setting for linear tensor product problems defined over Hilbert spaces. We assume that the domain space is a reproduc…
Product rules are optimal for numerical integration in classical smoothness spaces
Aicke Hinrichs, Erich Novak, Mario Ullrich +1
We mainly study numerical integration of real valued functions defined on the -dimensional unit cube with all partial derivatives up to some finite order bounded by one.…
-approximation in Korobov spaces with Exponential Weights
Peter Kritzer, Friedrich Pillichshammer, Henryk Wozniakowski
We study multivariate -approximation for a weighted Korobov space of periodic functions for which the Fourier coefficients decay exponentially fast. The we…
Tractability of Multivariate Problems for Standard and Linear Information in the Worst Case Setting: Part I
Erich Novak, Henryk Wozniakowski
We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functio…