12 citations · 20 across the 10 of their papers we have counts for
12 papers
On alternative quantization for doubly weighted approximation and integration over unbounded domains
P. Kritzer, F. Pillichshammer, L. Plaskota +1
It is known that for a -weighted -approximation of single variable functions with the th derivatives in a -weighted space, the minimal error of approximatio…
On efficient weighted integration via a change of variables
Peter Kritzer, Friedrich Pillichshammer, Leszek Plaskota +1
In this paper, we study the approximation of -dimensional -weighted integrals over unbounded domains or using a special change of variables, s…
Embeddings for Infinite-Dimensional Integration and -Approximation with Increasing Smoothness
M. Gnewuch, M. Hefter, A. Hinrichs +2
We study integration and -approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, whic…
Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals
Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens +1
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of -variate functions. Such -variate…
Truncation in Average and Worst Case Settings for Special Classes of -Variate Functions
Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski
The paper considers truncation errors for functions of the form , i.e., errors of approximating by $f_k(x_1,\dots,x_k)=g(\sum_{j…
Truncation Dimension for Linear Problems on Multivariate Function Spaces
Aicke Hinrichs, Peter Kritzer, Friedrich Pillichshammer +1
The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are: When is it possible to approximate the solutio…
Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in
Michael Gnewuch, Mario Hefter, Aicke Hinrichs +2
We consider -weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in a weighted norm with . The domain…
Truncation Dimension for Function Approximation
Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski
We consider approximation of functions of variables, where is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approxima…
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…
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…
Infinite-dimensional integration and the multivariate decomposition method
Frances Y. Kuo, Dirk Nuyens, Leszek Plaskota +2
We further develop the \emph{Multivariate Decomposition Method} (MDM) for the Lebesgue integration of functions of infinitely many variables with respect to a…
Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure
Grzegorz W. Wasilkowski
We study the average case complexity of multivariate integration and function approximation for the class of continuous functions of variables. The class $…