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Orthogonal Polynomials and their Applications pp 1–19Cite as

Error estimate in pade approximation

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1329))

Abstract

The aim of this paper is to extend Kronrod's procedure for estimating the error in Gaussian quadrature formulas to Padé approximation. Some results on Stieltjes polynomials are also given. Examples show the effectiveness of the method. The procedure is then applied to the ɛ-algorithm, which is a convergence acceleration method related to Padé approximation. General principles for estimating the error in series approximations and sequence transformations are also brought to light.

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References

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Author information

Authors and Affiliations

  1. Laboratoire d'Analyse Numérique et d'Optimisation U.F.R. I.E.E.A., Université des Sciences et Techniques de Lille Flandres-Artois, 59655, Villeneuve d'Ascq - Cedex, France

    Claude Brezinski

Authors
  1. Claude Brezinski
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Editor information

Manuel Alfaro Jesús S. Dehesa Francisco J. Marcellan José L. Rubio de Francia Jaime Vinuesa

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© 1988 Springer-Verlag

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Brezinski, C. (1988). Error estimate in pade approximation. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083350

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  • DOI: https://doi.org/10.1007/BFb0083350

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19489-7

  • Online ISBN: 978-3-540-39295-8

  • eBook Packages: Springer Book Archive

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