Approximants de Padé et séries hypergéométriques équilibrées
نویسندگان
چکیده
منابع مشابه
Padé Approximants in Complex Points Revisited
In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...
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Let µ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in C \ I and r(∞) = 0. We consider multipoint rational interpolants of the function f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...
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Résumé. L’utilisation d’un algorithme d’apprentissage non supervisé de type k-Means sur un jeu de séries temporelles amène à se poser deux questions : Celle du choix d’une mesure de similarité et celle du choix d’une méthode effectuant l’agrégation de plusieurs séries afin d’en estimer le centre (i.e. calculer les k moyennes). Afin de répondre à la première question, nous présentons dans cet ar...
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متن کاملAlgebraic properties of robust Padé approximants
For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called spurious poles, that is, poles with a close-by zero or poles with small residuals. A black box procedure for eliminating spurious poles would have a major impa...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2003
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(03)00027-8