Truncation Error Bounds for the Branched Continued Fraction [Formula omitted]

We analyze the problem of estimation of the error of approximation of a branched continued fraction, which is a multidimensional generalization of a continued fraction. By the method of fundamental inequalities, we establish truncation error bounds for the branched continued fraction[summation]i1=1Nai11+[summation]i2=1i1ai21+[summation]i3=1i2ai31+[midline horizontal ellipsis] whose elements belong to certain rectangular sets in the complex plane. The obtained results are applied to multidimensional S- and A-fractions with independent variables.