58 citations · 246 across the 21 of their papers we have counts for
21 papers
Computable error bounds for quasi-Monte Carlo using points with non-negative local discrepancy
Michael Gnewuch, Peter Kritzer, Art B. Owen +1
Let be a completely monotone integrand as defined by Aistleitner and Dick (2015) and let points hav…
New Bounds for the Extreme and the Star Discrepancy of Double-Infinite Matrices
Jasmin Fiedler, Michael Gnewuch, Christian Weiß
According to Aistleitner and Weimar, there exist two-dimensional (double) infinite matrices whose star-discrepancy of the first rows and columns, interpreted as…
Infinite-dimensional integration and -approximation on Hermite spaces
Michael Gnewuch, Aicke Hinrichs, Klaus Ritter +1
We study integration and -approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor prod…
Infinite-Variate -Approximation with Nested Subspace Sampling
Kumar Harsha, Michael Gnewuch, Marcin Wnuk
We consider -approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admi…
On Negative Dependence Properties of Latin Hypercube Samples and Scrambled Nets
Benjamin Doerr, Michael Gnewuch
We study the notion of -negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to -negative depe…
Discrepancy Bounds for a Class of Negatively Dependent Random Points Including Latin Hypercube Samples
Michael Gnewuch, Nils Hebbinghaus
We introduce a class of -negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin…
A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy
Michael Gnewuch, Hendrik Pasing, Christian Weiß
We prove a generalized Faulhaber inequality to bound the sums of the -th powers of the first (possibly shifted) natural numbers. With the help of this inequality we are able…
Randomized sparse grid algorithms for multivariate integration on Haar-Wavelet spaces
Marcin Wnuk, Michael Gnewuch
The \emph{deterministic} sparse grid method, also known as Smolyak's method, is a well-established and widely used tool to tackle multivariate approximation problems, and there is…
On Negatively Dependent Sampling Schemes, Variance Reduction, and Probabilistic Upper Discrepancy Bounds
Michael Gnewuch, Marcin Wnuk, Nils Hebbinghaus
We study some notions of negative dependence of a sampling scheme that can be used to derive variance bounds for the corresponding estimator or discrepancy bounds for the underlyin…
Note on Pairwise Negative Dependence of Randomized Rank-1 Lattices
Marcin Wnuk, Michael Gnewuch
In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence…
Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration
Michael Gnewuch, Marcin Wnuk
Smolyak's method, also known as hyperbolic cross approximation or sparse grid method, is a powerful tool to tackle multivariate tensor product problems solely with the help of effi…
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…
Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples
Benjamin Doerr, Carola Doerr, Michael Gnewuch
We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds…
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…
Embeddings of Weighted Hilbert Spaces and Applications to Multivariate and Infinite-Dimensional Integration
Michael Gnewuch, Mario Hefter, Aicke Hinrichs +1
We study embeddings and norm estimates for tensor products of weighted reproducing kernel Hilbert spaces. These results lead to a transfer principle that is directly applicable to…
Calculation of Discrepancy Measures and Applications
Carola Doerr, Michael Gnewuch, Magnus Wahlström
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepa…
Infinite-Dimensional Integration in Weighted Hilbert Spaces: Anchored Decompositions, Optimal Deterministic Algorithms, and Higher Order Convergence
Josef Dick, Michael Gnewuch
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matc…
Lower Error Bounds for Randomized Multilevel and Changing Dimension Algorithms
Michael Gnewuch
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, w…
Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition
Jan Baldeaux, Michael Gnewuch
In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decompositi…
A Randomized Algorithm Based on Threshold Accepting to Approximate the Star Discrepancy
Michael Gnewuch, Magnus Wahlström, Carola Winzen
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. An…
Construction of Minimal Bracketing Covers for Rectangles
Michael Gnewuch
We construct explicit -bracketing covers with minimal cardinality for the set system of (anchored) rectangles in the two dimensional unit cube. More precisely, the cardinality o…