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 {eλpz}kp=0, where {λp}kp=0 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 {epz}kp=0.
Keywords:
diagonal Hermite–Padé approximation of type I, system of exponential functions {eλpz}kp=0,
zeros of polynomials.
Citation:
A. P. Starovoitov, E. P. Kechko, “Upper Bounds for the Moduli of Zeros of Hermite–Padé Approximations for a Set of Exponential Functions”, Mat. Zametki, 99:3 (2016), 409–420; Math. Notes, 99:3 (2016), 417–425
\Bibitem{StaKec16}
\by A.~P.~Starovoitov, E.~P.~Kechko
\paper Upper Bounds for the Moduli of Zeros of Hermite--Pad\'e Approximations for a Set of Exponential Functions
\jour Mat. Zametki
\yr 2016
\vol 99
\issue 3
\pages 409--420
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\jour Math. Notes
\yr 2016
\vol 99
\issue 3
\pages 417--425
\crossref{https://doi.org/10.1134/S0001434616030111}
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Linking options:
https://www.mathnet.ru/eng/mzm10668
https://doi.org/10.4213/mzm10668
https://www.mathnet.ru/eng/mzm/v99/i3/p409
This publication is cited in the following 5 articles:
M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78
A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244
M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74
A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288
A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333
Citation in format AMSBIB
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