Computing Characteristic Polynomials of Matrices of Structured Polynomials

Abstract

We present a parallel modular algorithm for finding characteristic polynomials of matrices with integer coefficient bivariate monomials. For each prime, evaluation and interpolation gives us the bridge between polynomial matrices and matrices over a finite field so that the Hessenberg algorithm can be used. After optimizations, we are able to save a significant amount of work by incremental Chinese remaindering and early termination.

Computing characteristic polynomials of matrices of structured polynomials

“…• Published and presented as a paper [11] at the 19th International Workshop on Computer Algebra in Scientific Computing (CASC), a conference held in Bucharest, Romania in September 2016.…”