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Matematicheskie Zametki, 2014, Volume 96, Issue 5, Pages 762–772
DOI: https://doi.org/10.4213/mzm10536 (Mi mzm10536) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Formulas for Rational Interpolation and Remainders

A. K. Ramazanov

Kaluga Branch of Bauman Moscow State Technical University
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DOI: https://doi.org/10.4213/mzm10536
Abstract: This paper deals with the existence of interpolating rational functions serving as Thiele continued fraction convergents and also presents the expression for the remainder for such rational interpolations. These problems are similar to multipoint Padé approximations. For the limit case, the expression for the remainder in diagonal Padé approximations at zero is obtained; also a sufficiently simple expression for the exact value of the remainder in the case of the function $\sqrt{1+z}$ is derived.
Keywords: rational interpolation, Thiele continued fraction, continued fraction convergents, Padé approximation, remainder in the diagonal Padé approximation.
Received: 14.02.2013
Revised: 20.09.2013
English version:
Mathematical Notes, 2014, Volume 96, Issue 5, Pages 767–776
DOI: https://doi.org/10.1134/S0001434614110157
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: A. K. Ramazanov, “Formulas for Rational Interpolation and Remainders”, Mat. Zametki, 96:5 (2014), 762–772; Math. Notes, 96:5 (2014), 767–776
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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