An operator approach to multipoint Padé approximations

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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 Padé approximants to Nevanlinna functions is proved. © 2008 Elsevier Inc. All rights reserved.

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Derevyagin, M. S., & Zhedanov, A. S. (2009). An operator approach to multipoint Padé approximations. Journal of Approximation Theory, 157(1), 70–88. https://doi.org/10.1016/j.jat.2008.07.002

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