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Documents authored by Müller-Gronbach, Thomas

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

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

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

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

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

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.04401.1
04401 Abstracts Collection – Algorithms and Complexity for Continuous

Authors: Thomas Müller-Gronbach, Erich Novak, Knut Petras, and Joseph F. Traub

Published in: Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005)

Abstract
From 26.09.04 to 01.10.04, the Dagstuhl Seminar ``Algorithms and Complexity for Continuous Problems'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas 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, Erich Novak, Knut Petras, and Joseph F. Traub. 04401 Abstracts Collection – Algorithms and Complexity for Continuous. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, pp. 1-21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{mullergronbach_et_al:DagSemProc.04401.1,
  author =	{M\"{u}ller-Gronbach, Thomas and Novak, Erich and Petras, Knut and Traub, Joseph F.},
  title =	{{04401 Abstracts Collection – Algorithms and Complexity for Continuous}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--21},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras 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.04401.1},
  URN =		{urn:nbn:de:0030-drops-1545},
  doi =		{10.4230/DagSemProc.04401.1},
  annote =	{Keywords: Complexity and regularization of ill-posed problems , nonlinear approximation , tractability of high-dimensional numerical problems quantum computing , stochastic computation and quantization , global optimization , differential and integral equations}
}
Document
DOI: 10.4230/DagSemProc.04401.2
04401 Summary – Algorithms and Complexity for Continuous Problems

Authors: Thomas Müller-Gronbach, Erich Novak, Knut Petras, and Joseph F. Traub

Published in: Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005)

Abstract
The goal of this workshop was to bring together researchers from different communities working on computational aspects of continuous problems. Continuous computational problems arise in many areas of science and engineering. Examples include path and multivariate integration, function approximation, optimization, as well as differential, integral, and operator equations. Understanding the complexity of such problems and constructing efficient algorithms is both important and challenging. The workshop was of a very interdisciplinary nature with invitees from, e.g., computer science, numerical analysis, discrete, applied, and pure mathematics, physics, statistics, and scientific computation. Many of the lectures were presented by Ph.D. students. Compared to earlier meetings, several very active research areas received more emphasis. These include Quantum Computing, Complexity and Tractability of high-dimensional problems, Stochastic Computation, and Quantization, which was an entirely new field for this workshop. Due to strong connections between the topics treated at this workshop many of the participants initiated new cooperations and research projects. For more details, see the pdf-file with the same title.
Cite as

Thomas Müller-Gronbach, Erich Novak, Knut Petras, and Joseph F. Traub. 04401 Summary – Algorithms and Complexity for Continuous Problems. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{mullergronbach_et_al:DagSemProc.04401.2,
  author =	{M\"{u}ller-Gronbach, Thomas and Novak, Erich and Petras, Knut and Traub, Joseph F.},
  title =	{{04401 Summary – Algorithms and Complexity for Continuous Problems}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras 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.04401.2},
  URN =		{urn:nbn:de:0030-drops-1530},
  doi =		{10.4230/DagSemProc.04401.2},
  annote =	{Keywords: Complexity and Regularization of Ill-Posed Problems , Non-Linear Approximation , Tractability of High-Dimensional Numerical Problems Quasi-Monte Carlo Methods , Quantum Computing , Stochastic Computation and Quantization , Global Optimization , Differential and Integral Equation}
}
Document
DOI: 10.4230/DagSemProc.04401.6
Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations

Authors: Klaus Ritter and Thomas Müller-Gronbach

Published in: Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005)

Abstract
We study algorithms for approximation of the mild solution of stochastic heat equations on the spatial domain ]0,1[^d. The error of an algorithm is defined in L_2-sense. We derive lower bounds for the error of every algorithm that uses a total of N evaluations of one-dimensional components of the driving Wiener process W. For equations with additive noise we derive matching upper bounds and we construct asymptotically optimal algorithms. The error bounds depend on N and d, and on the decay of eigenvalues of the covariance of W in the case of nuclear noise. In the latter case the use of non-uniform time discretizations is crucial.
Cite as

Klaus Ritter and Thomas Müller-Gronbach. Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, pp. 1-37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{ritter_et_al:DagSemProc.04401.6,
  author =	{Ritter, Klaus and M\"{u}ller-Gronbach, Thomas},
  title =	{{Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--37},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras 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.04401.6},
  URN =		{urn:nbn:de:0030-drops-1518},
  doi =		{10.4230/DagSemProc.04401.6},
  annote =	{Keywords: Stochastic heat equation , Non-uniform time discretization , minimal errors , upper and lower bounds}
}
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