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Rational approximation of analytic functions

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Abstract

The paper provides an overview of the author’s contribution to the theory of constructive rational approximations of analytic functions. The results presented are related to the convergence theory of Padé approximants and of more general rational interpolation processes, which significantly expand the classical theory’s framework of continuous fractions, to inverse problems in the theory of Padé approximants, to the application of multipoint Padé approximants (solutions of Cauchy-Jacobi interpolation problem) in explorations connected with the rate of Chebyshev rational approximation of analytic functions and to the asymptotic properties of Padé-Hermite approximation for systems of Markov type functions.

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References

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Authors and Affiliations

  1. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. A. Gonchar

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  1. A. A. Gonchar
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Original Russian Text © A.A. Gonchar, 2003, published in Sovremennye Problemy Matematiki, 2003, Vol. 1, pp. 83–106.

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Gonchar, A.A. Rational approximation of analytic functions. Proc. Steklov Inst. Math. 272 (Suppl 2), 44–57 (2011). https://doi.org/10.1134/S0081543811030047

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