Existence and uniqueness of rational interpolants with free and prescribed poles

  • Herbert Stahl
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1287)


We study existence and uniqueness problems associated with different definitions of rational interpolants with free or prescribed poles. The treatment of the subject is rather general; it includes interpolation at infinity, at confluent points, and interpolation in polar singularities.


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  1. 1.
    Baker, G.A. Jr. and Graves-Morris, P.R. (1981): Padé Approximants, Part I and II. Encycl. of Math. Vol. 13 and 14, Cambridge Univ. Press, Cambridge.Google Scholar
  2. 2.
    Brezinski, C. (1981): The long history of continued fractions and Padé approximants. In: Padé Approximants and Applications. (de Bruin, M.G. and van Rossum, H., eds), Lect. Notes Math., Vol. 888, Springer-Verlag, Berlin 1–27.Google Scholar
  3. 3.
    Claessens, G. (1978): On the structure of the Newton-Padé table. J. Approx. Theory 22, 304–319.CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Cauchy, A.L. (1821): Sur la formulae de Lagrange relative à l’interpolation. Analyse algebraique, Paris.Google Scholar
  5. 5.
    Jacobi, C.G.I. (1846): Ueber die Darstellung einer Reihe gegebener Werte durch eine gebrochene rationale Funktion. Crelle’s J. reine u. angew. Math. 30, 127–156.CrossRefzbMATHGoogle Scholar
  6. 6.
    Kronecker, L. (1881): Zur Theorie der Elimination einer Variabeln aus zwei algebraischen Gleichungen. Monatsb. koenigl. Preuss. Akad. Wiss. Berlin, 535–600.Google Scholar
  7. 7.
    Meinguet, J. (1970): On the solubility of the Cauchy interpolation problem. In: Approximation Theory (Talbot, A., ed.), Academic Press, London, 137–163.Google Scholar
  8. 8.
    Perron, O. (1929): Die Lehre von den Kettenbruechen. Chelsea Pub. Co., New York.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Herbert Stahl
    • 1
  1. 1.TU-Berlin/Sekr. FR 6–8Berlin 10Fed. Rep. Germany

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