An operator approach to multipoint Padé approximations

  • Authors:

  • Maxim S. Derevyagin;Alexei S. Zhedanov

  • Affiliations:

  • Department of Nonlinear Analysis, Institute of Applied Mathematics and Mechanics, R.Luxemburg Street 74, 83114 Donetsk, Ukraine;Institute for Physics and Engineering, R.Luxemburg Street 72, 83114 Donetsk, Ukraine

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2009

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Abstract

First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result, a convergence theorem for multipoint Pade approximants to Nevanlinna functions is proved.