An application of reduce to the approximation of F(X,Y)

  • C. Chaffy-Camus
Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 358)

Abstract

Padé approximants are an important tool in numerical analysis, to evaluate f(x) from its power series even outside the disk of convergence, or to locate its singularities. This paper generalizes this process to the multivariate case and presents two applications of this method: the approximation of implicit curves and the approximation of double power series. Computations absolutely need to be carried out on a computer algebra system.

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References

  1. [1]
    G.A. BAKER. P.R. GRAVES-MORRIS: Padé approximants. I Basic theory. II Extensions and applications, Encyclopedia of Mathematics and applications, vol 13 (1981)Google Scholar
  2. [2]
    C. CHAFFY: Une construction "homogène" d'approximants de Padé à deux variables, Num. Math. vol 45 (1984) p 149–164Google Scholar
  3. [3]
    C. CHAFFY: Les approximants de (Padé) rond (Padé): un théorème de convergence, RR 685M. TIM3 IMAG (décembre 1987)Google Scholar
  4. [4]
    J.S.R. CHISHOLM: Rational approximants defined from double power series, Math. Comp. 27 (1973) p 841–848Google Scholar
  5. [5]
    A.A.M. CUYT: Padé approximants for operators: theory and applications, Lecture Notes in Maths, no 1065. Springer Verlag (1984)Google Scholar
  6. [6]
    P.R. GRAVES-MORRIS: Generalizations of the theorem of de Montessus de Ballore using Canterburry approximants, in "Padé and rational approximation: theory and applications" Saff, Varga eds. Academic Press (1977) p 73–82Google Scholar
  7. [7]
    J. KARLSSON H. WALLIN: Rational interpolation by an interpolation procedure in several variables, in "Padé and rational approximation: theory and applications" Saff, Varga eds. Academic Press (1977) p 83–100Google Scholar
  8. [8]
    C.H. LUTTERODT: Rational approximants to holomorphic functions in n dimensions, J. Math. Anal. Appl. 53 (1976) p 89–98Google Scholar
  9. [9]
    R. MONTESSUS DE BALLORE: Sur les fractions continues algébriques, Rend. di Palermo 19 (1905) p 1–73Google Scholar
  10. [10]
    E.B. SAFF: An extension of Montessus de Ballore's theorem on the convergence of interpolation rational functions, J. Approx. Theory 6 (1972) p 63–67Google Scholar
  11. [11]
    R. WILSON: Divergent continued fractions and polar singularities. Proc. London Math. Soc. 26 (1927) p 159–168Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • C. Chaffy-Camus
    • 1
  1. 1.Algoparallèle et calcul formel TIM3 - INPGGrenoble cedexFrance

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