Geodesic
Formulas for Rational Interpolation and Remainders
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 762-772 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : rational interpolation, Padé approximation
Keywords: Thiele continued fraction, continued fraction convergents, remainder in the diagonal Padé approximation. 
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A. K. Ramazanov. Formulas for Rational Interpolation and Remainders. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 762-772. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a11/

[1] U. Dzhouns, V. Tron, Nepreryvnye drobi. Analiticheskaya teoriya i prilozheniya, Mir, M., 1985 | MR

[2] T. N. Thiele, “Bemärkninger om periodiske Kjädebrökers Konvergens”, Zeuthen Tidsskr. (4), 3 (1879) | Zbl

[3] Dzh. Beiker ml., P. Greivs-Morris, Approksimatsii Pade. Ch. 1. Osnovy teorii. Ch. 2. Obobscheniya i prilozheniya, Mir, M., 1986 | MR | Zbl

[4] G. Korn, T. Korn, Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. Opredeleniya, teoremy, formuly, Nauka, M., 1970

[5] N. E. Nörlund, Vorlesungen über Differenzenrechnung, Grundlehren Math. Wiss., 13, Springer, Berlin, 1924 | Zbl

[6] V. K. Dzyadyk, L. I. Filozof, “O skorosti skhodimosti approksimatsii Pade dlya nekotorykh elementarnykh funktsii”, Matem. sb., 107:3 (1978), 347–363 | MR | Zbl

[7] Y. L. Luke, The Special Functions and Their Approximations, Math. Sci. Eng., 53, Academic Press, New York, London, 1969 | MR | MR | Zbl