Numerische Mathematik

, Volume 43, Issue 2, pp 293–307

General order Newton-Padé approximants for multivariate functions

  • Annie A. M. Cuyt
  • Brigitte M. Verdonk
Article

DOI: 10.1007/BF01390129

Cite this article as:
Cuyt, A.A.M. & Verdonk, B.M. Numer. Math. (1984) 43: 293. doi:10.1007/BF01390129

Summary

Padé approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off(x1, ...,xp). Therefore multivariate Newton-Padé approximants are introduced; their computation will only use the value off at some points. In Sect. 1 we shall repeat the univariate Newton-Padé approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Padé approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that forp=1 the classical Newton-Padé approximants for a univariate function are obtained.

Subject Classifications

AMS(MOS): 65D15 CR: 5.13 

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Annie A. M. Cuyt
    • 1
  • Brigitte M. Verdonk
    • 1
  1. 1.Department of Mathematics U.I.A.Universiteitsplein 1WilrijkBelgium

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