Direct and Inverse Results on Row Sequences of Hermite–Padé Approximants

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants...

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Veröffentlicht in:Constructive approximation 2013-08, Vol.38 (1), p.133-160
Hauptverfasser: Cacoq, J., de la Calle Ysern, B., López Lagomasino, G.
Format: Artikel
Sprache:eng
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Zusammenfassung:We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided.
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-013-9188-0