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Multipoints rational approximants

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

Abstract

We consider multipoints rational approximants of a function f analytic near zero, with arbitrary poles αi. We show that the choice of \(1\sqrt \alpha _i\) as interpolation points, leads to a sequence of approximants which converges uniformly and geometrically to £.

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References

  1. C. BREZINSKI-Rational approximation to formal power series. J. of approx theory Vol. 25 no 4 April 79.

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  2. M. GALLUCCI-W.B. JONES-Rational approximation corresponding to Newton series (Newton Padé approximants). J. of approx theory 17.366–392 (1976).

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  3. M. B. FARES-Sur l’approximation rationnelle de fonctions de variable complexe au sens de la norme de Hardy. Thèse de 3ème cycle Grenoble 1982.

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  4. J. VAN ISEGHEM-Applications des approximants de type Padé. Thèse de 3ème cycle Lille 1982.

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  5. J.L. WALSH-Interpolation and approximation by rational functions in the complex domains. AMS coll. Pub. XX.

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Helmut Werner Hans Josef Bünger

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© 1984 Springer-Verlag

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van Iseghem, J. (1984). Multipoints rational approximants. 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/BFb0099616

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  • DOI: https://doi.org/10.1007/BFb0099616

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13364-3

  • Online ISBN: 978-3-540-38914-9

  • eBook Packages: Springer Book Archive

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