Systems of linear equations with dense univariate polynomial coefficients

Abstract

An algorithm for computing the power series solution of a system of linear equations with components that are dense univariate polynomials over a field is described and analyzed. A method for converting the power series solution to rational form is derived. Theoretical and experimental cost estimates are obtained and used to identify classes of problems for which the power series method outperforms modular methods. Finally, it is shown that the power series method also provides an effective mechanism for solving the problem in which the coefficients of the polynomials are from the ring of integers.