Volume

Dagstuhl Seminar Proceedings, Volume 9391

Publication Details

  • published at: 2009-12-02
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.09391.1
09391 Abstracts Collection – Algorithms and Complexity for Continuous Problems

Authors: Thomas Müller-Gronbach, Leszek Plaskota, and Joseph F. Traub

Abstract
From 20.09.09 to 25.09.09, the Dagstuhl Seminar 09391 Algorithms and Complexity for Continuous Problems was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Thomas Müller-Gronbach, Leszek Plaskota, and Joseph F. Traub. 09391 Abstracts Collection – Algorithms and Complexity for Continuous Problems. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 9391, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{mullergronbach_et_al:DagSemProc.09391.1,
  author =	{M\"{u}ller-Gronbach, Thomas and Plaskota, Leszek and Traub, Joseph F.},
  title =	{{09391 Abstracts Collection – Algorithms and Complexity for Continuous Problems}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--23},
  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.09391.1},
  URN =		{urn:nbn:de:0030-drops-23005},
  doi =		{10.4230/DagSemProc.09391.1},
  annote =	{Keywords: Computational complexity of continuous problems, partial information, high-dimensional problems, tractability analysis, quasi-Monte Carlo methods, op operator equations, non-linear approximation, stochastic computation, ill posed-problems}
}
Document
DOI: 10.4230/DagSemProc.09391.2
Discrepancy Bounds for Mixed Sequences

Authors: Michael Gnewuch

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.09391.3
Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea

Authors: Fred J. Hickernell, Thomas Müller-Gronbach, Ben Niu, and Klaus Ritter

Abstract
Prices of path dependent options may be modeled as expectations of functions of an infinite sequence of real variables. This talk presents recent work on bounding the error of such expectations using quasi-Monte Carlo algorithms. The expectation is approximated by an average of $n$ samples, and the functional of an infinite number of variables is approximated by a function of only $d$ variables. A multilevel algorithm employing a sum of sample averages, each with different truncated dimensions, $d_l$, and different sample sizes, $n_l$, yields faster convergence than a single level algorithm. This talk presents results in the worst-case error setting.
Cite as

Fred J. Hickernell, Thomas Müller-Gronbach, Ben Niu, and Klaus Ritter. Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 9391, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{hickernell_et_al:DagSemProc.09391.3,
  author =	{Hickernell, Fred J. and M\"{u}ller-Gronbach, Thomas and Niu, Ben and Ritter, Klaus},
  title =	{{Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--19},
  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.09391.3},
  URN =		{urn:nbn:de:0030-drops-22987},
  doi =		{10.4230/DagSemProc.09391.3},
  annote =	{Keywords: Brownian motions, multilevel, option pricing, worst-case error}
}
Document
DOI: 10.4230/DagSemProc.09391.4
Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases

Authors: Krzysztof Sikorski, Bhagirath Addepalli, E. R. Pardyjak, and M. Zhdanov

Abstract
An inversion technique based on MC/QMC search and regularized gradient optimization was developed to solve the atmospheric source characterization problem. The Gaussian Plume Model was adopted as the forward operator and QMC/MC search was implemented in order to find good starting points for the gradient optimization. This approach was validated on the Copenhagen Tracer Experiments. The QMC approach with the utilization of clasical and scrambled Halton, Hammersley and Sobol points was shown to be 10-100 times more efficient than the Mersenne Twister Monte Carlo generator. Further experiments are needed for different data sets. Computational complexity analysis needs to be carried out .
Cite as

Krzysztof Sikorski, Bhagirath Addepalli, E. R. Pardyjak, and M. Zhdanov. Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 9391, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{sikorski_et_al:DagSemProc.09391.4,
  author =	{Sikorski, Krzysztof and Addepalli, Bhagirath and Pardyjak, E. R. and Zhdanov, M.},
  title =	{{Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases }},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--19},
  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.09391.4},
  URN =		{urn:nbn:de:0030-drops-22998},
  doi =		{10.4230/DagSemProc.09391.4},
  annote =	{Keywords: Atmospheric source problem, Gaussian Plume Model, Quasi Monte Carlo method, gradient optimization}
}
Document
DOI: 10.4230/DagSemProc.09391.5
Weighted L_2 B Discrepancy and Approximation of Integrals over Reproducing Kernel Hilbert Spaces

Authors: Michael Gnewuch

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}
}

Filters

  • Authors
  • A
  • Addepalli, Bhagirath
  • G
  • Gnewuch, Michael
  • H
  • Hickernell, Fred J.
  • M
  • Müller-Gronbach, Thomas
  • N
  • Niu, Ben
  • P
  • Pardyjak, E. R.
  • Plaskota, Leszek
  • R
  • Ritter, Klaus
  • S
  • Sikorski, Krzysztof
  • T
  • Traub, Joseph F.
  • Z
  • Zhdanov, M.

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