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The Usual Behaviour of Rational Approximations

Published online by Cambridge University Press:  20 November 2018

Peter B. Borwein
Peter B. Borwein*
Affiliation:
Dalhousie University Halifax, Nova Scotia Canada B3H 4H8
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Abstract

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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.

Keywords

41 A20A21A25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 317 - 323
Copyright
Copyright © Canadian Mathematical Society 1983

References

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