Geodesic
Upper Bounds for the Moduli of Zeros of Hermite--Pad\'e Approximations for a Set of Exponential Functions
Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 409-420

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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 $\{e^{pz}\}_{p=0}^k$.
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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     author = {A. P. Starovoitov and E. P. Kechko},
     title = {Upper {Bounds} for the {Moduli} of {Zeros} of {Hermite--Pad\'e} {Approximations} for a {Set} of {Exponential} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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A. P. Starovoitov; E. P. Kechko. Upper Bounds for the Moduli of Zeros of Hermite--Pad\'e Approximations for a Set of Exponential Functions. Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 409-420. http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a10/