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Advances in Computational Mathematics

, Volume 7, Issue 3, pp 199–233 | Cite as

The Petrov–Galerkin method for second kind integral equations II: multiwavelet schemes

  • Zhongying Chen
  • Charles A. Micchelli
  • Yuesheng Xu
Article

Abstract

This paper continues the theme of the recent work [Z. Chen and Y. Xu, The Petrov–Galerkin and iterated Petrov–Galerkin methods for second kind integral equations, SIAM J. Numer. Anal., to appear] and further develops the Petrov–Galerkin method for Fredholm integral equations of the second kind. Specifically, we study wavelet Petrov–Galerkin schemes based on discontinuous orthogonal multiwavelets and prove that the condition number of the coefficient matrix for the linear system obtained from the wavelet Petrov–Galerkin scheme is bounded. In addition, we propose a truncation strategy which forms a basis for fast wavelet algorithms and analyze the order of convergence and computational complexity of these algorithms.

Keywords

Cond Condition Number Galerkin Method Wavelet Base Fredholm Integral Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Zhongying Chen
    • 1
  • Charles A. Micchelli
    • 2
  • Yuesheng Xu
    • 3
  1. 1.Department of Scientific ComputationZhongshan UniversityGuangzhouP.R.China
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA
  3. 3.Department of MathematicsNorth Dakota State UniversityFargoUSA

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