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Titlebook: Nonlinear Numerical Methods and Rational Approximation II; Annie Cuyt Book 1994 Springer Science+Business Media Dordrecht 1994 Meromorphic

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楼主: retort
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Recurrence Relations in the Table of Vector Orthogonal PolynomialsVector orthogonal polynomials appeared as the denominators of vector approximants ([2]). To compute these last ones or to study the orthogonality itself, it is useful to be able to move in the table of the polynomials. It is obviously the first step before studying non regular cases of vector-orthogonality.
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Padé-Type Approximants and Multivariate Polynomial InterpolationPadé-type approximants of a formal power series can be automatically derived from polynomial interpolants of some generating function of this series. Several examples are given, with special emphasis on Hakopian’s multivariate polynomial interpolants of types I and II.
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Matrix Rational Interpolation with Poles as Interpolation Pointsuivalence provides an effective method for computing matrix rational interpolants having poles as interpolation points. However, this equivalence is only valid in those cases where enough pole information is known. It is an open problem on how one can transform the pole problem to a no-pole problem in other cases.
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