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Sparse Grids and Applications

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Jochen Garcke

    1. , Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

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  2. Michael Griebel

    1. Inst. Numerische Simulation, Universität Bonn, Bonn, Germany

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 88)

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Table of contents (13 papers)

  1. Front Matter

    Pages i-x
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  2. An Adaptive Sparse Grid Approach for Time Series Prediction

    • Bastian Bohn, Michael Griebel
    Pages 1-30

  3. Efficient Analysis of High Dimensional Data in Tensor Formats

    • Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko, Hermann G. Matthies, Elmar Zander
    Pages 31-56

  4. Sparse Grids in a Nutshell

    • Jochen Garcke
    Pages 57-80

  5. Intraday Foreign Exchange Rate Forecasting Using Sparse Grids

    • Jochen Garcke, Thomas Gerstner, Michael Griebel
    Pages 81-105

  6. Dimension- and Time-Adaptive Multilevel Monte Carlo Methods

    • Thomas Gerstner, Stefan Heinz
    Pages 107-120

  7. An Efficient Sparse Grid Galerkin Approach for the Numerical Valuation of Basket Options Under Kou’s Jump-Diffusion Model

    • Michael Griebel, Alexander Hullmann
    Pages 121-150

  8. The Use of Sparse Grid Approximation for the r-Term Tensor Representation

    • Wolfgang Hackbusch
    Pages 151-159

  9. On Multilevel Quadrature for Elliptic Stochastic Partial Differential Equations

    • Helmut Harbrecht, Michael Peters, Markus Siebenmorgen
    Pages 161-179

  10. Local and Dimension Adaptive Stochastic Collocation for Uncertainty Quantification

    • John D. Jakeman, Stephen G. Roberts
    Pages 181-203

  11. The Combination Technique for the Initial Value Problem in Linear Gyrokinetics

    • Christoph Kowitz, Dirk Pflüger, Frank Jenko, Markus Hegland
    Pages 205-222

  12. Model Reduction with the Reduced Basis Method and Sparse Grids

    • Benjamin Peherstorfer, Stefan Zimmer, Hans-Joachim Bungartz
    Pages 223-242

  13. Spatially Adaptive Refinement

    • Dirk Pflüger
    Pages 243-262

  14. Asymptotic Expansion Around Principal Components and the Complexity of Dimension Adaptive Algorithms

    • Christoph Reisinger
    Pages 263-276

  15. Back Matter

    Pages 277-283
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Keywords

About this book

In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.

Editors and Affiliations

  • , Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Jochen Garcke

  • Inst. Numerische Simulation, Universität Bonn, Bonn, Germany

    Michael Griebel

About the editors

Jochen Garcke is Professor at the Institute of Numerical Simulation, University of Bonn. Michael Griebel is Managing Editor of the journal Numerische Mathematik, series editor of LNCSE and volume editor of the proceedings on Meshfree Methods for PDEs, published as LNCSE 43, 57, 65 and 79.

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