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Documents authored by Gnewuch, Michael

Document
DOI: 10.4230/DagRep.13.8.106
Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 23351)

Authors: Dmitriy Bilyk, Michael Gnewuch, Jan Vybíral, Larisa Yaroslavtseva, and Kumar Harsha

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
The Dagstuhl Seminar 23351 was held at the Leibniz Center for Informatics, Schloss Dagstuhl, from August 27 to September 1, 2023. This event was the 14th in a series of Dagstuhl Seminars, starting in 1991. During the seminar, researchers presented overview talks, recent research results, work in progress and open problems. The first section of this report describes the goal of the seminar, the main seminar topics, and the general structure of the seminar. The third section contains the abstracts of the talks given during the seminar and the forth section the problems presented at the problem session.
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Dmitriy Bilyk, Michael Gnewuch, Jan Vybíral, Larisa Yaroslavtseva, and Kumar Harsha. Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 23351). In Dagstuhl Reports, Volume 13, Issue 8, pp. 106-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{bilyk_et_al:DagRep.13.8.106,
  author =	{Bilyk, Dmitriy and Gnewuch, Michael and Vyb{\'\i}ral, Jan and Yaroslavtseva, Larisa and Harsha, Kumar},
  title =	{{Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 23351)}},
  pages =	{106--128},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Bilyk, Dmitriy and Gnewuch, Michael and Vyb{\'\i}ral, Jan and Yaroslavtseva, Larisa and Harsha, Kumar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.106},
  URN =		{urn:nbn:de:0030-drops-198152},
  doi =		{10.4230/DagRep.13.8.106},
  annote =	{Keywords: computational stochastics, infinite-variate problems, quasi-\{M\}onte \{C\}arlo, sampling, tractability analysis}
}
Document
DOI: 10.4230/DagSemProc.09391.2
Discrepancy Bounds for Mixed Sequences

Authors: Michael Gnewuch

Published in: Dagstuhl Seminar Proceedings, Volume 9391, Algorithms and Complexity for Continuous Problems (2009)

Abstract
A mixed sequence is a sequence in the $s$-dimensional unit cube which one obtains by concatenating a $d$-dimensional low-discrepancy sequence with an $s-d$-dimensional random sequence. We discuss some probabilistic bounds on the star discrepancy of mixed sequences.
Cite as

Michael Gnewuch. Discrepancy Bounds for Mixed Sequences. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 9391, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{gnewuch:DagSemProc.09391.2,
  author =	{Gnewuch, Michael},
  title =	{{Discrepancy Bounds for Mixed Sequences}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9391},
  editor =	{Thomas M\"{u}ller-Gronbach and Leszek Plaskota and Joseph. F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09391.2},
  URN =		{urn:nbn:de:0030-drops-22975},
  doi =		{10.4230/DagSemProc.09391.2},
  annote =	{Keywords: Star Discrepancy, Mixed Sequence, Hybrid Method, Monte Carlo, Quasi-Monte Carlo, Probabilistic Bounds}
}
Document
DOI: 10.4230/DagSemProc.09391.5
Weighted L_2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces

Authors: Michael Gnewuch

Published in: Dagstuhl Seminar Proceedings, Volume 9391, Algorithms and Complexity for Continuous Problems (2009)

Abstract
We extend the notion of $L_2$ $B$ discrepancy provided in [E. Novak, H. Wo'zniakowski, $L_2$ discrepancy and multivariate integration, in: Analytic number theory. Essays in honour of Klaus Roth. W. W. L. Chen, W. T. Gowers, H. Halberstam, W. M. Schmidt, and R. C. Vaughan (Eds.), Cambridge University Press, Cambridge, 2009, 359 – 388] to the weighted $L_2$ $mathcal{B}$ discrepancy. This newly defined notion allows to consider weights, but also volume measures different from the Lebesgue measure and classes of test sets different from measurable subsets of some Euclidean space. We relate the weighted $L_2$ $mathcal{B}$ discrepancy to numerical integration defined over weighted reproducing kernel Hilbert spaces and settle in this way an open problem posed by Novak and Wo'zniakowski.
Cite as

Michael Gnewuch. Weighted L_2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 9391, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{gnewuch:DagSemProc.09391.5,
  author =	{Gnewuch, Michael},
  title =	{{Weighted L\underline2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9391},
  editor =	{Thomas M\"{u}ller-Gronbach and Leszek Plaskota and Joseph. F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09391.5},
  URN =		{urn:nbn:de:0030-drops-22966},
  doi =		{10.4230/DagSemProc.09391.5},
  annote =	{Keywords: Discrepancy, Numerical Integration, Quasi-Monte Carlo, Reproducing Kernel Hilbert Space}
}
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