Extraction of Quantifiable Information from Complex Systems

  • Stephan Dahlke
  • Wolfgang Dahmen
  • Michael Griebel
  • Wolfgang Hackbusch
  • Klaus Ritter
  • Reinhold Schneider
  • Christoph Schwab
  • Harry Yserentant

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 102)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Denis Belomestny, Christian Bender, Fabian Dickmann, Nikolaus Schweizer
    Pages 1-23
  3. Wolfgang Dahmen, Chunyan Huang, Gitta Kutyniok, Wang-Q Lim, Christoph Schwab, Gerrit Welper
    Pages 25-51
  4. Rudolf Ressel, Patrick Dülk, Stephan Dahlke, Kamil S. Kazimierski, Peter Maass
    Pages 53-67
  5. Nabi G. Chegini, Stephan Dahlke, Ulrich Friedrich, Rob Stevenson
    Pages 69-81
  6. Petru A. Cioica, Stephan Dahlke, Nicolas Döhring, Stefan Kinzel, Felix Lindner, Thorsten Raasch et al.
    Pages 83-107
  7. Martin Altmayer, Steffen Dereich, Sangmeng Li, Thomas Müller-Gronbach, Andreas Neuenkirch, Klaus Ritter et al.
    Pages 109-132
  8. Oliver G. Ernst, Björn Sprungk, Hans-Jörg Starkloff
    Pages 133-159
  9. Joscha Diehl, Peter K. Friz, Hilmar Mai, Harald Oberhauser, Sebastian Riedel, Wilhelm Stannat
    Pages 161-178
  10. Jochen Garcke, Irene Klompmaker
    Pages 179-194
  11. Jonas Ballani, Lars Grasedyck, Melanie Kluge
    Pages 195-210
  12. Michael Griebel, Jan Hamaekers, Frederik Heber
    Pages 211-235
  13. Wolfgang Hackbusch, Reinhold Schneider
    Pages 237-261
  14. Leonardo Jost, Simon Setzer, Matthias Hein
    Pages 263-279
  15. Mijail Guillemard, Dennis Heinen, Armin Iske, Sara Krause-Solberg, Gerlind Plonka
    Pages 281-302
  16. Lutz Kämmerer, Stefan Kunis, Ines Melzer, Daniel Potts, Toni Volkmer
    Pages 347-363
  17. Evelyn Herrholz, Dirk Lorenz, Gerd Teschke, Dennis Trede
    Pages 365-379
  18. Christian Lubich
    Pages 381-396

About this book

Introduction

In April 2007, the  Deutsche Forschungsgemeinschaft (DFG) approved the  Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program.
 
Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance.  Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges.
 
Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program.
 
The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and, as such, they allowed us to use closely related approaches.

 

Keywords

complex systems computational stochastics high-dimensional problems numerical analysis

Editors and affiliations

  • Stephan Dahlke
    • 1
  • Wolfgang Dahmen
    • 2
  • Michael Griebel
    • 3
  • Wolfgang Hackbusch
    • 4
  • Klaus Ritter
    • 5
  • Reinhold Schneider
    • 6
  • Christoph Schwab
    • 7
  • Harry Yserentant
    • 8
  1. 1.FB 12 Mathematik und InformatikPhilipps-Universität MarburgMarburgGermany
  2. 2.Inst. Geometrie & Praktische MathemathikRWTH Aachen UniversityAachenGermany
  3. 3.Universität Bonn Institut für Numerische SimulationBonnGermany
  4. 4.Max-Planck-Inst. f. Mathem. in d. NaturwissenschaftenLeipzigGermany
  5. 5.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany
  6. 6.Institut für MathematikTechnische Universität BerlinBerlinGermany
  7. 7.Seminar für Angewandte MathematikETH ZürichZürichSwitzerland
  8. 8.Institut für MathematikTechnische Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-08159-5
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08158-8
  • Online ISBN 978-3-319-08159-5
  • Series Print ISSN 1439-7358
  • Series Online ISSN 2197-7100
  • About this book