Open AccessA multidimensional generalization of the Rutishauser $qd$-algorithm
Author(s) -
R. I. Dmytryshyn
Publication year - 2016
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.8.2.230-238
Subject(s) - generalization , mathematics , fraction (chemistry) , series (stratigraphy) , algorithm , multidimensional systems , discrete mathematics , mathematical analysis , paleontology , chemistry , organic chemistry , biology
In this paper the regular multidimensional $C$-fraction with independent variables, which is a generalization of regular $C$-fraction, is considered. An algorithm of calculation of the coefficients of the regular multidimensional $C$-fraction with independent variables correspondence to a given formal multiple power series is constructed. Necessary and sufficient conditions of the existence of this algorithm are established. The above mentioned algorithm is a multidimensional generalization of the Rutishauser $qd$-algorithm.