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Some properties and applications of Chebyshev polynomial and rational approximation

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Rational Approximation and Interpolation

Part of the book series: Lecture Notes in Mathematics ((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 Several new or unpublished ideas are introduced in these areas.

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Authors and Affiliations

  1. Department of Mathematics and Ballistics, Royal Military College of Science Shrivenham, Swindon, Wiltshire, England

    JC Mason

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  1. JC Mason
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Peter Russell Graves-Morris Edward B. Saff Richard S. Varga

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© 1984 Springer-Verlag

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Mason, J. (1984). Some properties and applications of Chebyshev polynomial and rational approximation. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072398

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  • DOI: https://doi.org/10.1007/BFb0072398

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13899-0

  • Online ISBN: 978-3-540-39113-5

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