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Russian Mathematical Surveys, 2002, Volume 57, Issue 1, Pages 43–141
DOI: https://doi.org/10.1070/RM2002v057n01ABEH000475 (Mi rm475) 		 
This article is cited in 96 scientific papers (total in 96 papers)

Padé approximants and efficient analytic continuation of a power series

S. P. Suetin

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (890 kB) Citations (96)
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DOI: https://doi.org/10.1070/RM2002v057n01ABEH000475
Abstract: This survey reflects the current state of the theory of Padé approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory, in which one must make deductions about analytic continuation of a given power series on the basis of the known asymptotic behaviour of the poles of some sequence of Padé approximants of this series. Row and diagonal sequences are studied from this point of view. Gonchar's and Rakhmanov's fundamental results of inverse nature are presented along with results of the author.
Received: 15.10.2001
Russian version:
Uspekhi Matematicheskikh Nauk, 2002, Volume 57, Issue 1(343), Pages 45–142
DOI: https://doi.org/10.4213/rm475
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 41A21, 30B40, 41A20; Secondary 30E25, 30F30, 30B70, 34M50, 14K20
Language: English
Original paper language: Russian
Citation: S. P. Suetin, “Padé approximants and efficient analytic continuation of a power series”, Uspekhi Mat. Nauk, 57:1(343) (2002), 45–142; Russian Math. Surveys, 57:1 (2002), 43–141
Citation in format AMSBIB
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    • This publication is cited in the following 96 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:138
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