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：本论文涉及通过分支连分数（特别是带有独立变量的多维A-和J-分数）逼近多元函数的问题。构建了Gragg算法的一个推广版本，它使我们能够通过给定的形式多元幂级数的系数计算相应的带独立变量的多维A-分数的系数。此算法还可以用于构造与给定形式多重Laurent级数对应的带独立变量的多维J-分数。给出了一些用这些分支连分数逼近多元函数的数值实验。
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