Upper Bounds for the Moduli of Zeros of Hermite--Pad\'e Approximations for a Set of Exponential Functions

A. P. Starovoitov ; E. P. Kechko

Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 409-420.

Résumé

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 $\{e^{\lambda_pz}\}_{p=0}^k$, where $\{\lambda_p\}_{p=0}^k$ 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 $\{e^{pz}\}_{p=0}^k$.

Détail

Keywords: diagonal Hermite–Padé approximation of type I, system of exponential functions $\{e^{\lambda_pz}\}_{p=0}^k$, zeros of polynomials.

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