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Sbornik: Mathematics, 2016, Volume 207, Issue 6, Pages 769–791
DOI: https://doi.org/10.1070/SM8470 (Mi sm8470) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Hermite-Padé approximation of exponential functions

A. V. Astafieva, A. P. Starovoitov

Francisk Skorina Gomel State University, Belarus
English version PDF (573 kB) Citations (8)
References:
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DOI: https://doi.org/10.1070/SM8470
Abstract: The paper is concerned with diagonal Hermite-Padé polynomials of the first kind for the system of exponentials $\{e^{\lambda_jz}\}_{j=0}^k$ with arbitrary distinct complex parameters $\{\lambda_k\}_{j=0}^k$. An asymptotic formula for the remainder term is established and the location of the zeros is described. For real parameters the asymptotics are found and the extremal properties are described. The theorems obtained supplement the well-known results due to Borwein, Wielonsky, Saff, Varga and Stahl.
Bibliography: 43 titles.
Keywords: system of exponentials, Padé polynomials, Hermite-Padé polynomials, asymptotic equalities, the Laplace method, the saddle-point method.
Funding agency Grant number
Ministry of Education of the Republic of Belarus
This research was carried out with the financial support of the Ministry of Education of the Republic of Belarus under the Federal Programme for Scientific Research for 2011–2015.
Received: 08.01.2015 and 20.03.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 6, Pages 3–26
DOI: https://doi.org/10.4213/sm8470
Bibliographic databases:
Document Type: Article
UDC: 517.538.52+517.538.53+517.518.84
MSC: 41A21
Language: English
Original paper language: Russian
Citation: A. V. Astafieva, A. P. Starovoitov, “Hermite-Padé approximation of exponential functions”, Mat. Sb., 207:6 (2016), 3–26; Sb. Math., 207:6 (2016), 769–791
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:465
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    References:65
    First page:37
     
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