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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.

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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}
}

@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.04401.5

Information-Based Nonlinear Approximation: An Average Case Setting

Authors: Leszek Plaskota

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

Abstract

Nonlinear approximation has usually been studied under deterministic assumption and complete information about the underlying functions. We assume only partial information and we are interested in the average case error and complexity of approximation. It turns out that the problem can be essentially split into two independent problems related to average case nonlinear (restricted) approximation from complete information, and average case unrestricted approximation from partial information. The results are then applied to average case piecewise polynomial approximation, and to average case approximation of real sequences.

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Leszek Plaskota. Information-Based Nonlinear Approximation: An Average Case Setting. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{plaskota:DagSemProc.04401.5,
  author =	{Plaskota, Leszek},
  title =	{{Information-Based Nonlinear Approximation: An Average Case Setting}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--1},
  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.04401.5},
  URN =		{urn:nbn:de:0030-drops-1504},
  doi =		{10.4230/DagSemProc.04401.5},
  annote =	{Keywords: average case setting , nonlinear approximation , information-based comlexity}
}

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09391 Abstracts Collection – Algorithms and Complexity for Continuous Problems

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Information-Based Nonlinear Approximation: An Average Case Setting

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