Geodesic
The Usual Behaviour of Rational Approximations
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 317-323

Voir la notice de l'article provenant de la source Cambridge University Press

Questions concerning the convergence of Padé and best rational approximations are considered from a categorical point of view in the complete metric space of entire functions. The set of functions for which a subsequence of the mth row of the Padé table converges uniformly on compact subsets of the complex plane is shown to be residual.The speed of convergence of best uniform rational approximations and Padé approximations on the unit disc is compared. It is shown that, in a categorical sense, it is expected that subsequences of these approximants will converge at the same rate.Likewise, it is expected that the poles of certain sequences of best uniform rational approximations wil be dense in the entire plane.
DOI : 10.4153/CMB-1983-051-1
Mots-clés : 41 A20, A21, A25 
Borwein, Peter B. The Usual Behaviour of Rational Approximations. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 317-323. doi: 10.4153/CMB-1983-051-1
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