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Constructive Approximation

, Volume 38, Issue 1, pp 133–160 | Cite as

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

  • J. Cacoq
  • B. de la Calle Ysern
  • G. López Lagomasino
Article

Abstract

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.

Keywords

Montessus de Ballore theorem Simultaneous approximation Hermite–Padé approximation Rate of convergence Inverse results 

Mathematics Subject Classification (2010)

30E10 41A21 41A28 41A25 41A27 

Notes

Acknowledgements

The work of B. de la Calle Ysern received support from MINCINN under grant MTM2009-14668-C02-02 and from UPM through Research Group “Constructive Approximation Theory and Applications”. The work of J. Cacoq and G. López was supported by Ministerio de Economía y Competitividad under grants MTM2009-12740-C03-01 and MTM2012-36372-C03-01.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • J. Cacoq
    • 1
  • B. de la Calle Ysern
    • 2
  • G. López Lagomasino
    • 1
  1. 1.Dpto. de Matemáticas, Escuela Politécnica SuperiorUniversidad Carlos III de MadridLeganésSpain
  2. 2.Dpto. de Matemática Aplicada, E. T. S. de Ingenieros IndustrialesUniversidad Politécnica de MadridMadridSpain

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