On Computing the Exact Determinant of Matrices with Polynomial Entries

Abstract

The problem of computing the determinant of a matrix of polynomials is considered. Four algorithms are compared- expansion by minors, Gausslan elimination over the integers, a method based on evaluation and interpolation, and a procedure which computes the characteristic polynomial of the matrix. Each method m analyzed with respect to its computing time and storage requirements using several models for polynomial growth. First, the asymptotic time and storage is developed for each method within each model. In addition to these asymptotm results, the analysis is done exactly for certain especially small, yet practical and important cases Then the results of empirical studies are given which support conclusions about which of the methods will work best within an actual computing environment. © 1975, ACM. All rights reserved.