The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is constructed that enables us to compute, by the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional A-fraction with independent variables. This algorithm can also be used to construct the multidimensional J-fraction with independent variables corresponding to a given formal multiple Laurent series. Some numerical experiments of approximating the functions of several variables by these branched continued fractions are given.

翻译：本文研究多变量函数的分支连分式逼近问题，重点探讨独立变量多维A-分式和J-分式。通过构建Gragg算法的推广形式，我们能够根据给定形式多重幂级数的系数，计算对应的独立变量多维A-分式的系数。该算法还可用于构造与给定形式多重洛朗级数相对应的独立变量多维J-分式。文中给出了利用这些分支连分式逼近多变量函数的若干数值实验。