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Exponential convergence
of a linear rational interpolant
between transformed Chebyshev points


Authors: Richard Baltensperger, Jean-Paul Berrut and Benjamin Noël
Journal: Math. Comp. 68 (1999), 1109-1120
MSC (1991): Primary 65D05, 41A20, 41A25
DOI: https://doi.org/10.1090/S0025-5718-99-01070-4
Published electronically: February 19, 1999
MathSciNet review: 1642809
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Abstract: In 1988 the second author presented experimentally well-conditioned linear rational functions for global interpolation. We give here arrays of nodes for which one of these interpolants converges exponentially for analytic functions


References [Enhancements On Off] (What's this?)

  • [Bal-Ber1] Baltensperger, R. and Berrut, J.-P.: The errors in calculating the pseudospectral differentiation matrices for Chebyshev-Gauss-Lobatto points, to appear in Comput. Math. Applic.
  • [Bal-Ber2] Baltensperger, R. and Berrut, J.-P.: The linear rational collocation method, submitted for publication.
  • [Ber1] Berrut, J.-P.: Rational functions for guaranteed and experimentally well-conditioned global interpolation, Comput. Math. Applic., 15, 1-16 (1988). MR 89b:65029
  • [Ber2] Berrut, J.-P.: Barycentric formulae for cardinal (SINC-) interpolants, Numer. Math., 54, 703-718 (1989) (Erratum 55, 747 (1989)). MR 90d:65025a,b
  • [Ber-Mit] Berrut, J.-P. and Mittelmann, H. D.: Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval, Comput. Math. Applic., 33, 77-86 (1997). MR 98c:41015
  • [Boy] Boyd, J. P.: Chebyshev and Fourier Spectral Methods, Springer Verlag, Berlin-Heidelberg-New York (1989).
  • [Hen] Henrici, P.: Essentials of Numerical Analysis with Pocket Calculator Demonstrations, Wiley, New York (1982). MR 83h:65002
  • [Kau-Kau] Kaup, L. and Kaup, B.: Holomorphic Functions of Several Variables, de Gruyter, Berlin-New York (1983). MR 85k:32001
  • [Kos-Tal] Kosloff, D. and Tal-Ezer, H.: A modified Chebyshev pseudospectral method with an ${\mathcal O}(N^{-1})$ time step restriction, J. Comput. Phys., 104, 457-469 (1993). MR 93k:65080
  • [Riv] Rivlin, T. J.: The Chebyshev Polynomials, Wiley, New York (1974). MR 56:9142
  • [Sal] Salzer, H. E.: Lagrangian interpolation at the Chebyshev points $x_{n,\nu}=\cos(\nu\pi/n),~\nu=0(1)n$; some unnoted advantages, The Computer J., 15, 156-159 (1972). MR 47:4414
  • [Sch-Wer] Schneider, C. and Werner, W.: Some new aspects of rational interpolation, Math. Comp., 47, 285-299 (1986). MR 87k:65012
  • [Sch] Schwarz, H. R.: Numerische Mathematik, 2te Aufl., Teubner, Stuttgart (1988); English translation: Numerical Analysis, A Comprehensive Introduction, Wiley, New-York (1989). MR 92a:65008; MR 90g:65003
  • [Sto] Stoer, J.: Einführung in die Numerische Mathematik I, 4te Aufl., Springer, Berlin (1983). MR 83d:65003 (3rd ed.)

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Additional Information

Richard Baltensperger
Affiliation: Institut de Mathématiques, Université de Fribourg, Pérolles, CH-1700 Fribourg, Switzerland
Email: richard.baltensperger@unifr.ch

Jean-Paul Berrut
Affiliation: Institut de Mathématiques, Université de Fribourg, Pérolles, CH-1700 Fribourg, Switzerland
Email: jean-paul.berrut@unifr.ch

Benjamin Noël
Affiliation: Institut de Mathématiques, Université de Fribourg, Pérolles, CH-1700 Fribourg, Switzerland

DOI: https://doi.org/10.1090/S0025-5718-99-01070-4
Keywords: Interpolation, rational interpolation, linear interpolation, exponential convergence
Received by editor(s): February 10, 1998
Published electronically: February 19, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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