New results on multivariate polynomial matrix factorizations

Multivariate (n-D) polynomial matrix factorizations are basic research problems in multidimensional systems and signal processing. In this paper several extensions of the existing results on multivariate matrix factorizations are proved. Moreover, by means of the general theory of multivariate matrix factorizations recently developed, a new proof is given to the bivariate polynomial matrix factorizations. This new approach produces also a recursive algorithm for the actual computation of the general bivariate matrix factorizations, which relies on the algorithm of the Gröbner bases for modules and does not involve calculations over the function fields.