45 citations · 84 across the 39 of their papers we have counts for
6 papers · 2 filters
Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces
Peter Hellekalek, Peter Kritzer, Friedrich Pillichshammer
In this paper, we study quasi-Monte Carlo (QMC) integration in weighted Sobolev spaces. In contrast to many previous results the QMC algorithms considered here are of open type, i.…
Numerical integration in -Korobov and -cosine spaces
Josef Dick, Peter Kritzer, Gunther Leobacher +1
QMC rules are equal weight quadrature rules for approximating integrals over . One line of research studies the integration error of functions in the unit ball of so-calle…
Tractability of multivariate analytic problems
Peter Kritzer, Friedrich Pillichshammer, Henryk Wozniakowski
In the theory of tractability of multivariate problems one usually studies problems with finite smoothness. Then we want to know which -variate problems can be approximated to w…
A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights
Josef Dick, Peter Kritzer, Gunther Leobacher +1
Lattice rules and polynomial lattice rules are quadrature rules for approximating integrals over the -dimensional unit cube. Since no explicit constructions of such quadrature m…
Tractability of multivariate integration in hybrid function spaces
Peter Kritzer, Friedrich Pillichshammer
We consider tractability of integration in reproducing kernel Hilbert spaces which are a tensor product of a Walsh space and a Korobov space. The main result provides necessary and…
Integration in Hermite spaces of analytic functions
Christian Irrgeher, Peter Kritzer, Gunther Leobacher +1
We study integration in a class of Hilbert spaces of analytic functions defined on the . The functions are characterized by the property that their Hermite coefficien…