Coprime fraction computation of 2-D rational matrices

Abstract

This note presents a numerical method of computing a coprime fraction of a two-dimensional (2-D) rational matrix, not necessarily proper. It is achieved by searching the primary linearly dependent rows, in order from top to bottom, of the two generalized resultants. The procedure can be extended to the three- or higher dimensional case and the result can also be used to compute the greatest common divisor (GCD) of 2-D polynomial matrices without employing primitive factorizations which does not exist in the three- or higher dimensional case.