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Mat. Zametki, 2014, Volume 96, Issue 5, Pages 762–772 (Mi mz10536)  

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

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.

DOI: https://doi.org/10.4213/mzm10536

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English version:
Mathematical Notes, 2014, 96:5, 767–776

Bibliographic databases:

UDC: 517.5
Received: 14.02.2013
Revised: 20.09.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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