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Rational Approximation and Interpolation pp 49–72Cite as

Polynomial, sinc and rational function methods for approximating analytic functions

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1105))

Abstract

This paper presents practically useful constructive linear methods of approximation of analytic functions by polynomials, sinc functions and rational functions. Spaces of functions of the type frequently encountered in applications are described for approximation by each method. Within these spaces, the rate of convergence of each approximation is nearly optimal.

Work supported by U.S. Army Research Contract No. DAAG29 83 K 0012.

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References

  1. Bernstein, S. and C. de la Vallee Poussin, L'Approximation, Chelsea, N.Y. (1970).

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  2. Burchard, H.G., and Höllig, W.G., N-Width and Entropy of H p-Classes in Lq(−1,1). To appear.

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  3. Magnus, W., Oberhettinger, F. and Soni, R.P., Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, N.Y. (1956).

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  4. National Bureau of Standards, Handbook of Mathematical Functions, N.B.S. Applied Math. Series 55 (1964).

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  5. Powell, M. J. D., Approximation Theory and Methods, Cambridge University Press (1981).

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  6. Stenger, F., Numerical Methods Based on the Whittaker Cardinal or Sinc Functions, SIAM Rev. 22 (1981) 165–224.

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  7. Stenger, F., Explicit, Nearly Optimal, Linear Rational Approximation with Preassigned Poles. Submitted for publication.

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Authors and Affiliations

  1. Department of Mathematics, University of Utah, 84112, Salt Lake City, Utah

    Frank Stenger

Authors
  1. Frank Stenger
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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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Stenger, F. (1984). Polynomial, sinc and rational function methods for approximating analytic functions. 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/BFb0072399

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  • DOI: https://doi.org/10.1007/BFb0072399

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13899-0

  • Online ISBN: 978-3-540-39113-5

  • eBook Packages: Springer Book Archive

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