Abstract
In the first 4 sections we discuss topics from univariate rational H ermite interpolation (URI). These topics include the structure of the table of URI, a recursive computation scheme and a continued fraction representation both in the normal case and the non-normal case and a convergence theorem for rational Hermite interpolants of meromorphic functions.
In the next 4 sections these items are generalized to the multivariate case. We first introduce multivariate rational Hermite interpolants (MRI) for data sets satisfying the inclusion property or rectangle rule and give a recursive computation scheme and a non-branched continued fraction representation, both for the non-degenerate and the degenerate case. For general data sets only results for ordinary rational interpolation in the case of non-degeneracy were obtained in [CUYTd].
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© 1992 Springer Science+Business Media Dordrecht
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Annie, C. (1992). Rational Hermite Interpolation in One and More Variables. In: Singh, S.P. (eds) Approximation Theory, Spline Functions and Applications. NATO ASI Series, vol 356. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2634-2_4
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DOI: https://doi.org/10.1007/978-94-011-2634-2_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5164-4
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