45 citations · 84 across the 39 of their papers we have counts for
9 papers · 1 filter
On Equivalence of Anchored and ANOVA Spaces; Lower Bounds
Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski
We provide lower bounds for the norms of embeddings between -weighted Anchored and ANOVA spaces of -variate functions with mixed partial derivatives of order one b…
Integration and approximation in cosine spaces of smooth functions
Christian Irrgeher, Peter Kritzer, Friedrich Pillichshammer
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case s…
Mixed orthogonal arrays, -nets, and -sequences
Peter Kritzer, Harald Niederreiter
We study the classes of -nets and -sequences, which are generalizations of -nets and -sequences, respectively. We show equivalence r…
From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules
Henri Faure, Peter Kritzer, Friedrich Pillichshammer
In 1935 J.G. van der Corput introduced a sequence which has excellent uniform distribution properties modulo 1. This sequence is based on a very simple digital construction scheme…
Approximation in Hermite spaces of smooth functions
Christian Irrgeher, Peter Kritzer, Friedrich Pillichshammer +1
We consider -approximation of elements of a Hermite space of analytic functions over . The Hermite space is a weighted reproducing kernel Hilbert space…
Very Low Truncation Dimension for High Dimensional Integration Under Modest Error Demand
P. Kritzer, F. Pillichshammer, G. W. Wasilkowski
We consider the problem of numerical integration for weighted anchored and ANOVA Sobolev spaces of -variate functions. Here is large including . Under the assumpti…