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Error estimate in pade approximation

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Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Orthogonal Polynomial
  • Gaussian Quadrature
  • Orthogonality Property
  • Sequence Transformation
  • Pade Approximant

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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References

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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

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