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Padé-type approximants for multivariate series of functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1071)

Abstract

Padé-type approximants (PTA) for multivariate series of functions \(f(t) = \mathop \Sigma \limits_{p = o}^{ + \infty } \mathop \Sigma \limits_{\left| i \right| = p} c_i g_i (t) (t \in \mathbb{R}^k ,i \in \mathbb{N}^k )\) are formally defined as c(P(.,t)) where P(x,t) are interpolating polynomials in IRk, in the sense of Hakopian, of the generating functions \(\mathop \Sigma \limits_{p = o}^\infty \mathop \Sigma \limits_{\left| p \right| = i} (\begin{array}{*{20}c}p \\i \\\end{array} ) x^i g_i (t)\) and where c is the linear form, associated with f, defined by \(c(x^i ) = c_i /(\begin{array}{*{20}c}p \\i \\\end{array} )\) for |i| = p. When g(x,t)=(1−x.t)−k (x.t = scalar product of × and t in IRk), we get rational functions whose singularities are hyperplanes in IRk. Some properties of these PTA are given together with some computational remarks and an example.

Keywords

  • Chebyshev Polynomial
  • Homogenous Polynomial
  • Formal Power Series
  • Interpolation Polynomial
  • MUltivariate Interpolation

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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© 1984 Springer-Verlag

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Sablonniere, P. (1984). Padé-type approximants for multivariate series of functions. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099622

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  • DOI: https://doi.org/10.1007/BFb0099622

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13364-3

  • Online ISBN: 978-3-540-38914-9

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