  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.
