Constructive Approximation

, 30:423

An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs

  • Tammo Jan Dijkema
  • Christoph Schwab
  • Rob Stevenson
Open AccessArticle

DOI: 10.1007/s00365-009-9064-0

Cite this article as:
Dijkema, T.J., Schwab, C. & Stevenson, R. Constr Approx (2009) 30: 423. doi:10.1007/s00365-009-9064-0

Abstract

Adaptive tensor product wavelet methods are applied for solving Poisson’s equation, as well as anisotropic generalizations, in high space dimensions. It will be demonstrated that the resulting approximations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that we may lose is independent of the space dimension n. The cost of producing these approximations will be proportional to their length with a constant factor that may grow with n, but only linearly.

Keywords

Adaptive wavelet methodsBest N-term approximationsTensor product approximationSparse gridsMatrix compressionOptimal computational complexity

Mathematics Subject Classification (2000)

41A2541A6342C4046B2865N30
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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Tammo Jan Dijkema
    • 1
  • Christoph Schwab
    • 2
  • Rob Stevenson
    • 3
  1. 1.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands
  2. 2.Seminar for Applied Mathematics, ETHZ HG G58.1ETH ZürichZürichSwitzerland
  3. 3.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands