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Upper bounds for the moduli of zeros of Hermite–Padé approximations for a set of exponential functions

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Abstract

In this paper, we establish upper bounds for the moduli of zeros of Hermite–Padé approximations of type I for a system of exponential functions \(\left\{ {{e^{{\lambda _{{p^z}}}}}} \right\}_{p = 0}^k\), where \(\left\{ {{\lambda _p}} \right\}_{p = 0}^k\) are various arbitrary complex numbers. The proved statements supplement and generalize well-known results due to Saff and Varga, as well as those due to Stahl and Wielonsky, on the behavior of zeros of Hermite–Padé approximations for a set of exponential functions \(\left\{ {{e^{pz}}} \right\}_{p = 0}^k\).

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Authors and Affiliations

  1. Skorina Gomel State University, Gomel, Belarus

    A. P. Starovoitov & E. P. Kechko

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  1. A. P. Starovoitov
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  2. E. P. Kechko
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Correspondence to A. P. Starovoitov.

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Original Russian Text © A. P. Starovoitov, E. P. Kechko, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 3, pp. 409–420.

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Starovoitov, A.P., Kechko, E.P. Upper bounds for the moduli of zeros of Hermite–Padé approximations for a set of exponential functions. Math Notes 99, 417–425 (2016). https://doi.org/10.1134/S0001434616030111

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