58 citations · 246 across the 21 of their papers we have counts for
Showing 2012 · math.NAShow all
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math.NA2012★ 25 cited
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…
math.NA2012
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…
math.NA2012★ 27 cited
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…