A multidimensional generalization of the Rutishauser $qd$-algorithm | Zendy

Roman Dmytryshyn | Zendy

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A multidimensional generalization of the Rutishauser $qd$-algorithm

Author(s) -

Roman Dmytryshyn

Publication year - 2016

Publication title -

carpathian mathematical publications

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.

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