Dagstuhl Seminar 06391
Algorithms and Complexity for Continuous Problems
( Sep 24 – Sep 29, 2006 )
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Organizers
- Stephan Dahlke (Universität Marburg, DE)
- Klaus Ritter (TU Darmstadt, DE)
- Ian H. Sloan (UNSW - Sydney, AU)
- Joseph F. Traub (Columbia University - New York, US)
Contact
The seminar was devoted to the branch of computational complexity that studies continuous problems for which only partial information is available. As an important example we mention an operator equation L x = y: here the right-hand side y and the coefficients of the (differential or integral) operator L are functions on some domain. These functions may only be evaluated at a finite number of properly chosen knots for the approximate computation of the solution x. Any such information about the coefficients is partial in the sense that it typically does not determine the solution x exactly.
The 8th Dagstuhl Seminar on Algorithms and Complexity of Continuous Problems attracted 50 participants from Computer Science and Mathematics, representing 11 countries and 4 continents. Among them have been 19 young researchers, some of whom have just received there diploma or master degree.
There were 43 presentations covering in particular the following topics:
- complexity and tractability of high-dimensional problems,
- complexity of operator equations and non-linear approximation,
- quantum computation,
- stochastic computation and quantization
- complexity of stochastic computation and quantization, and
- complexity and regularization of ill-posed problems,
together with applications in financial engineering and computer graphics. Abstracts are included in these Seminar Proceedings.
In addition to the substantial number of young participants another key feature of the seminar was the interaction between scientists working in different areas, namely, numerical analysis and scientific computing, probability theory and statistics, number theory, and theoretical computer science. In particular, distinguished researchers from numerical analysis were invited, and the mutual exchange of ideas was very inspiring and created many new ideas. Especially, one of the most challenging features of modern numerical analysis is the treatment of high-dimensional problems which requires several new paradigma. It has turned out that many developments that have been achieved in the IBC-community such as high-dimensional quadrature etc. will probably play a central role in this context, so that merging together the different approaches and ideas will be a very exciting topic in the near future.
Moreover, the meeting helped us to create new and to maintain the already existing various collaborations. Some ideas devoloped at the meeting have already flown into joint applications for reseach grants.
The organizers would like to thank all the attendees for their participation, and the Dagstuhl team for the excellent working environment and the hospitality at the Schloss.
- Howard Barnum (Los Alamos National Lab., US)
- Arvid Bessen (Columbia University - New York, US)
- Volker Bosserhoff (Universität der Bundeswehr - München, DE)
- James M. Calvin (NJIT - Newark, US) [dblp]
- Hui Cao (RICAM - Linz, AT)
- Ronald Cools (KU Leuven, BE) [dblp]
- Jakob Creutzig (TU Darmstadt, DE)
- Stephan Dahlke (Universität Marburg, DE) [dblp]
- Ronald A. DeVore (University of South Carolina, US) [dblp]
- Josef Dick (UNSW - Sydney, AU) [dblp]
- Stefan Geiss (University of Jyväskylä, FI) [dblp]
- Michael Gnewuch (Christian-Albrechts-Universität zu Kiel, DE) [dblp]
- Maciej Gocwin (AGH Univ. of Science & Technology-Krakow, PL)
- Stefan Heinrich (TU Kaiserslautern, DE) [dblp]
- Aicke Hinrichs (Universität Jena, DE) [dblp]
- Peter Hoyer (University of Calgary, CA) [dblp]
- Boleslaw Z. Kacewicz (AGH Univ. of Science & Technology-Krakow, PL)
- Alexander Keller (mental images - Berlin, DE) [dblp]
- Peter Kritzer (Universität Salzburg, AT) [dblp]
- Frances Y. Kuo (UNSW - Sydney, AU) [dblp]
- Shuai Lu (RICAM - Linz, AT)
- 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)
- Bernhard Milla (TU Kaiserslautern, DE)
- Thomas Müller-Gronbach (Universität Magdeburg, DE) [dblp]
- Andreas Neuenkirch (TU Darmstadt, DE) [dblp]
- Erich Novak (Universität Jena, DE) [dblp]
- Dirk Nuyens (KU Leuven, BE) [dblp]
- Anargyros Papageorgiou (Columbia University - New York, US) [dblp]
- Sergei Pereverzyev (RICAM - Linz, AT) [dblp]
- Friedrich Pillichshammer (Universität Linz, AT) [dblp]
- Leszek Plaskota (University of Warsaw, PL) [dblp]
- Thorsten Raasch (Universität Marburg, DE)
- Klaus Ritter (TU Darmstadt, DE) [dblp]
- Wolfgang Ch. Schmid (Universität Salzburg, AT)
- Reinhold Schneider (Universität Kiel, DE)
- Winfried Sickel (Universität Jena, DE) [dblp]
- Krzysztof Sikorski (University of Utah - Salt Lake City, US)
- Ian H. Sloan (UNSW - Sydney, AU) [dblp]
- Rob Stevenson (Utrecht University, NL)
- Marek Szczesny (AGH Univ. of Science & Technology-Krakow, PL)
- Shu Tezuka (Kyushu University, JP)
- Joseph F. Traub (Columbia University - New York, US) [dblp]
- Jan Vybíral (Universität Jena, DE) [dblp]
- Tim Wagner (TU Darmstadt, DE)
- Grzegorz Wasilkowski (University of Kentucky - Lexington, US) [dblp]
- Ben J. Waterhouse (UNSW - Sydney, AU)
- Przemyslaw Wojtaszczyk (University of Warsaw, PL)
- Henryk Wozniakowski (Columbia University - New York, US) [dblp]
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Classification
- Continuous algorithms/complexity
Keywords
- Continuous algorithms
- Continuous complexity
- Tractability
- High-dimensional problems
- Operator equations
- Quantum computation
- Stochastic computation
- Ill-posed problems
- Monte Carlo
- Qubit complexity
- Random noise
- Approximation theory
- Lattice rules
