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Numerical Algorithms

, Volume 5, Issue 9, pp 453–464 | Cite as

Fast algorithms for discrete Chebyshev-Vandermonde transforms and applications

  • Manfred Tasche
Part II Applications 9. Integrals and Integral Equations

Abstract

Applying orthogonal polynomials, the discrete Chebyshev-Vandermonde transform (DCVT) is introduced as a special almost orthogonal transform. An important example of DCVT is the discrete cosine transform (DCT). Using the divide-and-conquer technique and the d'Alembert functional equation, fast DCT-algorithms are described. By the help of these results we present for the first time fast, numerically stable algorithms for simultaneous polynomial approximation and for collocation method for the airfoil equation, a special Cauchytype singular integral equation.

Keywords

Integral Equation Functional Equation Discrete Cosine Transform Orthogonal Polynomial Fast Algorithm 
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

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Manfred Tasche
    • 1
  1. 1.Fachbereich MathematikUniversitÄt RostockRostockGermany

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