The Vector QD Algorithm for Smooth Functions (f, f′)

We deal with the functionz↦(f(z), f′(z)) wheref(z)=∑i⩾0aizi, (ai∈C) with limi→∞ai+1×ai−1/(ai)2=q. We investigate the convergence of the vector QD algorithm. We give the asymptotic behaviour of the generalized Hankel determinants. A convergence result on the vector orthogonal polynomials is proved....

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Vydané v:	Journal of approximation theory Ročník 86; číslo 3; s. 255 - 269
Hlavný autor:	Le Ferrand, Hervé
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.09.1996 Elsevier
Predmet:	Mathematics Numerical Analysis
ISSN:	0021-9045, 1096-0430
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Popis
Shrnutí:	We deal with the functionz↦(f(z), f′(z)) wheref(z)=∑i⩾0aizi, (ai∈C) with limi→∞ai+1×ai−1/(ai)2=q. We investigate the convergence of the vector QD algorithm. We give the asymptotic behaviour of the generalized Hankel determinants. A convergence result on the vector orthogonal polynomials is proved.
ISSN:	0021-9045 1096-0430
DOI:	10.1006/jath.1996.0067