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Asymptotics of Hermite-Padé Polynomials

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Progress in Approximation Theory

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 19))

Abstract

We review results about the asymptotic behavior (in the strong and weak sense) of Hermite-Padé polynomials of type II (also known as German polynomials). The polynomials appear as numerators and denominators of simultaneous rational approximants. The survey begins with general remarks on Hermite-Padé polynomials and a short summary of the state of the theory in this field.

Research supported in part ny the Deutsche Forschungsgemeinschaft (AZ: Sta 299 14-1).

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Authors and Affiliations

  1. Keldysh Institute, Moscow, Russia

    A. I. Aptekarev

  2. TFH/FB2, Luxemburger Str. 10, D-1000, Berlin 65, Germany

    Herbert Stahl

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  1. A. I. Aptekarev
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  2. Herbert Stahl
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Editors and Affiliations

  1. Steklov Mathematics Institute, 117966, Moscow GSP-1, Russia

    A. A. Gonchar

  2. Institute for Constructive Mathematics, University of South Florida, 33620, Tampa, FL, USA

    E. B. Saff

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Aptekarev, A.I., Stahl, H. (1992). Asymptotics of Hermite-Padé Polynomials. In: Gonchar, A.A., Saff, E.B. (eds) Progress in Approximation Theory. Springer Series in Computational Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2966-7_6

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