An algorithm for constructing multidimensional continued fractions and linear dependence of numbers

详细

The Güting algorithm for constructing multidimensional continued fractions is considered. It is proved that, in the case of dimension 2, this algorithm can be used to find the coefficients of the linear dependence of numbers; a criterion is given for verifying that the partial quotients furnished by the algorithmare, indeed, elements of the continued fraction for the expanded (generally irrational) numbers.