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Dagstuhl Seminar 02401

Algorithms and Complexity for Continuous Problems

( Sep 29 – Oct 04, 2002 )

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Continuous computational problems arise in diverse areas of science and engineering. There is great interest in computational aspects of multivariate problems. Examples include path and multivariate integration, function approximation, optimization, differential, integral and operator equations. Understanding the complexity of such problems and construction of efficient algorithms is both important and challenging.

An exciting area of research is algorithms and complexity for quantum computation. There will be a number of talks in this area. The study of quantum algorithms and complexity for continuous problems was recently initiated and will be discussed.

A major focus of the Workshop will continue to be the complexity of high dimensional problems and their tractability. Efficient or, ideally, optimal algorithms will be presented. Since Monte Carlo and/or quasi-Monte Carlo algorithms are often used for such problems, their efficiency will be addressed. There will be a number of talks on applications to finance. Models of computation and various settings (e.g., worst case, average case, or probabilistic) are important parts of the complexity study and these will be discussed as well.

Selected papers from the workshop will be published in a special issue of the Journal of Complexity.


Theoretical and applied research on algorithms and complexity for continuous problems


The seminar was devoted to the computational solution of continuous problems. Concrete algorithms and their analysis were discussed as well as complexity results were presented. Important continuous problems arise in different areas, and different techniques for analysis of these problems are necessary. Therefore the seminar attracted researchers from computer science, mathematics and applied mathematics, and statistics. There were altogether 46 participants representing 13 countries, among them 20 from Germany and 8 from the US. Together with senior and well recognized scientists, young prospective colleagues, some of them having just finished their diploma or master thesis, were also invited and presented their results.

A substantial part of the talks were devoted to numerical integration, with emphasis on problems with a large number of variables, and the algorithms under investigation were mainly Monte Carlo or quasi Monte Carlo methods. In some of these talks the computer-based construction of good deterministic cubature formulas was addressed.

A number of talks dealt with non-linear or operator equations, the latter being sometimes analyzed in a statistical setting with noisy data. Probabilistic concepts also played a role as a tool for analysis, e.g., for a problem from computational geometry or for global optimization, or as a part of the problem formulation itself, e.g., for solving stochastic differential equations.

Recently a new quantum model of computation has been introduced. Since quantum computers are potentially much more powerful than the classical ones, the quantum model is attracting great attention. At the Dagstuhl seminar 00931 in 2000 the first result concerning quantum algorithms for continuous problems was presented. Thereafter the quantum model has been included into several research projects related to the topics of the seminar. The current question is for what continuous problems the quantum model of computation offers an essential speed-up in solving them. There were 6 talks in which results on quantum complexity of summation, function approximation and integration were presented.

A selection of results presented at this conference will be published as invited papers in the Journal of Complexity.

The IBFI invited participants to a ceremony during our seminar, since Joe Traub, one of the seminar’s organizers, had his 70th birthday in 2002. We are grateful for this exceptional event, as well as for excellent working environment, the support, and the hospitality at Schloss Dagstuhl.

  • Emanouil Atanassov (Academy of Sciences - Sofia, BG)
  • Arvid Bessen (Columbia University - New York, US)
  • Karl-Heinz Borgwardt (Universität Augsburg, DE)
  • James M. Calvin (NJIT - Newark, US) [dblp]
  • Ronald Cools (KU Leuven, BE) [dblp]
  • Jakob Creutzig (TU Darmstadt, DE)
  • Stephan Dahlke (Universität Marburg, DE) [dblp]
  • Alexander Goldenshluger (Haifa University, IL)
  • Hilde Govaert (KU Leuven, BE)
  • Stefan Heinrich (TU Kaiserslautern, DE) [dblp]
  • Peter Hertling (Universität der Bundeswehr - München, DE) [dblp]
  • Norbert Hofmann (Aareal Bank AG - Wiesbaden, DE)
  • Matthias U. Horn (Universität Jena, DE)
  • Stefan Jaschke (Weierstraß Institut - Berlin, DE)
  • Boleslaw Z. Kacewicz (AGH Univ. of Science & Technology-Krakow, PL)
  • Reinhold Kainhofer (TU Graz, AT)
  • Aneta Karaivanova (Academy of Sciences - Sofia, BG)
  • Alexander Keller (Universität Ulm, DE) [dblp]
  • Peter Kloeden (Universität Frankfurt, DE)
  • Marek Kwas (Univ. of Inf. Technology & Management - Rzeszow, PL)
  • Peter Mathé (Weierstraß Institut - Berlin, DE) [dblp]
  • Klaus Meer (University of Southern Denmark - Odense, DK) [dblp]
  • Hrushikesh N. Mhaskar (California State Univ. - Los Angeles, US)
  • Thomas Müller-Gronbach (Universität Magdeburg, DE) [dblp]
  • Erich Novak (Universität Jena, DE) [dblp]
  • Anargyros Papageorgiou (Columbia University - New York, US) [dblp]
  • Sergei Pereverzyev (RICAM - Linz, AT) [dblp]
  • Knut Petras (Bergische Universität Wuppertal, DE)
  • Harald Pfeiffer (Universität Jena, DE)
  • Friedrich Pillichshammer (Universität Linz, AT) [dblp]
  • Allan Pinkus (Technion - Haifa, IL)
  • Leszek Plaskota (University of Warsaw, PL) [dblp]
  • Klaus Ritter (TU Darmstadt, DE) [dblp]
  • Wolfgang Ch. Schmid (Universität Salzburg, AT)
  • Arjen Sevenster (Elsevier Publishing - Amsterdam, NL)
  • Spencer Shellman (Los Alamos National Lab., US)
  • Winfried Sickel (Universität Jena, DE) [dblp]
  • Ian H. Sloan (UNSW - Sydney, AU) [dblp]
  • Ingo Steinwart (Universität Jena, DE) [dblp]
  • Vladimir N. Temlyakov (University of South Carolina, US) [dblp]
  • Shu Tezuka (Kyushu University, JP)
  • Joseph F. Traub (Columbia University - New York, US) [dblp]
  • Grzegorz Wasilkowski (University of Kentucky - Lexington, US) [dblp]
  • Carsten Wiegand (TU Kaiserslautern, DE)
  • Henryk Wozniakowski (Columbia University - New York, US) [dblp]
  • Peixin Ye (Chinese Academy of Sciences, CN)

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