General order Newton-Padé approximants for multivariate functions |
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Authors: | Annie A M Cuyt Brigitte M Verdonk |
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Institution: | (1) Department of Mathematics U.I.A., Universiteitsplein 1, B-2610 Wilrijk, Belgium |
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Abstract: | 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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Keywords: | AMS(MOS): 65D15 CR: 5 13 |
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