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A note on the rate of convergence of poles of generalized Hermite-Padé approximants. (English) Zbl 1463.30175

Summary: We consider row sequences of three generalized Hermite-Padé approximations (orthogonal Hermite-Padé approximation, Hermite-Padé-Faber approximation, and multipoint Hermite-Padé approximation) of a vector of the approximated functions \(\mathbf{F}\) and prove that if \(\mathbf{F}\) has a system pole of order \(\nu \), then such system pole attracts at least \(\nu\) zeros of denominators of these approximants at the rate of a geometric progression. Moreover, the rates of these attractions are estimated.

MSC:

30E10 Approximation in the complex plane
41A21 Padé approximation
41A25 Rate of convergence, degree of approximation
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References:

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