Quadrature Formulas for Refinable Functions and Wavelets II: Error Analysis

  • Arne Barinka
  • Titus Barsch
  • Stephan Dahlke
  • Mario Mommer
  • Michael Konik


This paper is concerned with the construction and the analysis of Gauss quadrature formulas for computing integrals of (smooth) functions against refinable functions and wavelets. The main goal of this paper is to develop rigorous error estimates for these formulas. For the univariate setting, we derive asymptotic error bounds for a huge class of weight functions including spline functions. We also discuss multivariate quadrature rules and present error estimates for specific nonseparable refinable functions, i.e., for some special box splines.

Gauss quadrature scaling functions wavelets splines error estimates 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Arne Barinka
    • 1
  • Titus Barsch
    • 1
  • Stephan Dahlke
    • 1
  • Mario Mommer
    • 1
  • Michael Konik
    • 2
  1. 1.RWTH AachenInstitut für Geometrie und Praktische MathematikAachenGermany
  2. 2.Fakultauml;t für MathematikTechnische Universität ChemnitzChemnitzGermany

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