Abstract
We first recall results from univariate Padé approximation theory (UPA). The recursive ∈-algorithm and the continued fraction representation obtained from the qd algorithm are given for the normal case as well as for a non-normal table composed of square blocks. Convergence of UPA for meromorphic functions and continuity of the univariate Padé operator are discussed.
The same approximation problem is considered in the multivariate case. General order multivariate Padé approximants (MPA) are defined and a recursive computation scheme and a continued fraction representation are given, both for the normal case and for the case of a table of MPA with degenerate solutions. A de Montessus de Ballore convergence theorem is presented and the continuity of the multivariate Padé operator is considered.
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Cuyt, A. (1992). Pade Approximation 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_3
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DOI: https://doi.org/10.1007/978-94-011-2634-2_3
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