Multivariate reciprocal differences for branched Thiele continued fraction expansions
For a multivariate function a Viscovatov-like algorithm for the construction of a branched continued fraction expansion was developed independently by \textit{J. A Murphy} and \textit{M. R. O'Donohoe} [ibid. 4, 181-190 (1978; Zbl 0407.40002)] and by \textit{K. J. Kuchminskaya} [Dopov. Akad. Nauk Ukr. RSR, Ser. A 1978, 613-617 (1978; Zbl 0418.40003)]. On the other hand, multivariate inverse difference to construct Thiele interpolating branched continued fractions were introduced independently by \textit{Kh. J. Kuchminskaya} [Mat. Metody Fiz.-Mekh. Polya 12, 3-10 (1980; Zbl 0439.41006)] and by the author of this paper [Computing 34, 41-61 (1985; Zbl 0553.41004)]. The purpose of this paper is to show the link between these two approaches in the multivariate case by introducing different multivariate reciprocal differences so as to obtain the branched continued fraction expansion as the limiting value of the Thiele interpolating branched continued fraction.
Thiele interpolating branched continued fractions
scientific article; zbMATH DE number 4041144