Parallel computation of determinants of matrices with polynomial entries

Abstract

An algorithm for computing the determinant of a matrix whose entries are multivariate polynomials is presented. It is based on classical multivariate Lagrange polynomial interpolation, and it exploits the Kronecker product structure of the coefficient matrix of the linear system associated with the interpolation problem. From this approach, the parallelization of the algorithm arises naturally. The reduction of the intermediate expression swell is also a remarkable feature of the algorithm.