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Some properties and applications of Chebyshev polynomial and rational approximation

  • JC Mason
Survey Articles
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

A number of key properties and applications of real and complex Chebyshev polynomials of the first and second kinds are here reviewed. First, in the overall context of Lp norms (1≤p≤∞), there is a review of the orthogonality and minimality properties of Chebyshev polynomials, the best and near-best approximation properties of Chebyshev series expansions and Chebyshev interpolating polynomials, and the links between Chebyshev series and Fourier and Laurent series. Second, there is a brief discussion of the applications of Chebyshev polynomials to Chebyshev-Padé-Laurent approximation, Chebyshev rational interpolation, Clenshaw-Curtis integration, and Chebyshev methods for integral and differential equations. Several new or unpublished ideas are introduced in these areas.

Keywords

Polynomial Approximation Chebyshev Polynomial Laurent Series Thomas Fermi Minimal Projection 
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

© Springer-Verlag 1984

Authors and Affiliations

  • JC Mason
    • 1
  1. 1.Department of Mathematics and BallisticsRoyal Military College of Science ShrivenhamSwindonEngland

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