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Padé-Type Approximants and Multivariate Polynomial Interpolation

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Book cover Nonlinear Numerical Methods and Rational Approximation II

Part of the book series: Mathematics and Its Applications ((MAIA,volume 296))

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Abstract

Padé-type approximants of a formal power series can be automatically derived from polynomial interpolants of some generating function of this series. Several examples are given, with special emphasis on Hakopian’s multivariate polynomial interpolants of types I and II.

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References

  1. B.D. Bojanov, H.A. Hakopian, A.A. Sahakian. Spline functions and multivariate interpolations. Kluwer, Dordrecht, 1993.

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  2. C. Brezinski. Padé approximants and general orthogonal polynomials. ISNM 50, Birkhäuser Verlag, Basel, 1980.

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  3. C. Brezinski, J. Van Iseghem. Padé approximations. To appear in Handbook of Numerical Analysis, Vol III, P.G. Ciarlet and J.L. Lions eds, North Holland.

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  4. H.A. Hakopian. Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type. J. Approx. Theory 34(1982), 286–305.

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  5. H.A. Hakopian. Multivariate interpolation II of Lagrange and Hermite type. Studia Mathematica 80(1984), 77–88.

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  6. P. Sablonnière. A new family of Padé-type approximants in ℝ k. J. Comp. Applied Math. 9 (1983), 347–359.

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  7. P. Sablonnière. Padé-type approximants for multivariate series of functions. in Padé approximation and its applications. H. Werner and H.J. Bürger eds, LNM 1071, Springer-Verlag, Berlin, 1984, 238–251.

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Author information

Authors and Affiliations

  1. Laboratoire LANS, INSA, 20, avenue des Buttes de Coësmes, 35043, Rennes Cédex, France

    Paul Sablonnière

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  1. Paul Sablonnière
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Annie Cuyt

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© 1994 Springer Science+Business Media Dordrecht

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Sablonnière, P. (1994). Padé-Type Approximants and Multivariate Polynomial Interpolation. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_12

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  • DOI: https://doi.org/10.1007/978-94-011-0970-3_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4420-2

  • Online ISBN: 978-94-011-0970-3

  • eBook Packages: Springer Book Archive

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