A multidimensional generalization of the Rutishauser $qd$-algorithm

Abstract

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.

Keywords

• regular multidimensional c-fraction with independent variables
• correspondence
• multiple power series
• algorithm