Geodesic
Formulas for Rational Interpolation and Remainders
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 762-772

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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
Keywords: Thiele continued fraction, continued fraction convergents, Padé approximation, remainder in the diagonal Padé approximation. 
@article{MZM_2014_96_5_a11,
     author = {A. K. Ramazanov},
     title = {Formulas for {Rational} {Interpolation} and {Remainders}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {762--772},
     publisher = {mathdoc},
     volume = {96},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a11/}
}
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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/