45 citations · 84 across the 39 of their papers we have counts for
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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…
Discrepancy estimates for index-transformed uniformly distributed sequences
Peter Kritzer, Gerhard Larcher, Friedrich Pillichshammer
In this paper we show discrepancy bounds for index-transformed uniformly distributed sequences. From a general result we deduce very tight lower and upper bounds on the discrepancy…
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…
Discrepancy bounds for low-dimensional point sets
Henri Faure, Peter Kritzer
The class of -nets and -sequences, introduced in their most general form by Niederreiter, are important examples of point sets and sequences that are commonly used…
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…