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Mat. Zametki, 2016, Volume 99, Issue 3, Pages 409–420 (Mi mz10668)  

This article is cited in 5 scientific papers (total in 5 papers)

Upper Bounds for the Moduli of Zeros of Hermite–Padé Approximations for a Set of Exponential Functions

A. P. Starovoitov, E. P. Kechko

Gomel State University named after Francisk Skorina

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

Funding Agency Grant Number
Ministry of Education of the Republic of Belarus
This work was supported by the Ministry of Education of Belarus within the framework of the State Program for Scientific Studies in 2011–2015.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm10668

Full text: PDF file (543 kB)
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English version:
Mathematical Notes, 2016, 99:3, 417–425

Bibliographic databases:

UDC: 517.538.52+517.538.53
Received: 18.02.2015
Revised: 18.09.2015

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

Citation in format AMSBIB
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\paper Upper Bounds for the Moduli of Zeros of Hermite--Pad\'e Approximations for a Set of Exponential Functions
\jour Mat. Zametki
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\vol 99
\issue 3
\pages 409--420
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\pages 417--425
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2017, no. 2(31), 69–74  mathnet
    2. A. P. Starovoitov, “Asymptotics of Diagonal Hermite–Padé Polynomials for the Collection of Exponential Functions”, Math. Notes, 102:2 (2017), 277–288  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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  mathnet  crossref  crossref  isi  elib
    4. A. P. Starovoitov, M. V. Sidortsov, A. A. Drapeza, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78  mathnet
    5. A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244  mathnet  crossref  crossref  isi  elib  elib
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