Optimal Degree Estimation of the Determinant of a Polynomial Matrix

Abstract

In this paper we present a recursive formula to find the degree of the determinant of a bivariate polynomial matrix. The proposed algorithm returns the optimal estimation of the degree but has a very large computational cost. The recursive formula can be represented as an assignment problem which is solved with the Hungarian method that has a very small computational cost. The contribution of the proposed formula is to reduce the required interpolation points for the evaluation–interpolation technique. That is, we reduce the evaluations which are computations of determinants or inverse matrices.