A Douglas-Shapiro-Shields factorization approach to the Leech equation

Abstract

In a recent series of papers concrete procedures were derived to compute a stable rational matrix solution to the Leech equation with rational matrix data. In one of these papers the procedure involved a specific Douglas-Shapiro-Shields (DSS) factorization. In the present paper it is shown that one can take a class of DSS factorizations as the starting point of the procedure, leading to solutions which may have a lower McMillan degree as the one obtained in the original procedure