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General order Newton-Padé approximants for multivariate functions

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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(x 1, ...,x p ). 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.

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Authors and Affiliations

  1. Department of Mathematics U.I.A., Universiteitsplein 1, B-2610, Wilrijk, Belgium

    Annie A. M. Cuyt (Research assistant of the National Fund for Scientific Research (Belgium) & Brigitte M. Verdonk

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  1. Annie A. M. Cuyt
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  2. Brigitte M. Verdonk
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Cuyt, A.A.M., Verdonk, B.M. General order Newton-Padé approximants for multivariate functions. Numer. Math. 43, 293–307 (1984). https://doi.org/10.1007/BF01390129

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