Numerical matrix methods in the computation of the greatest common divisor (GCD) of polynomials

Abstract

In this research, the method for computing the GCD of two polynomials in the orthogonal basis, using the comrade matrix approach is further investigated. Generally, polynomials in the orthogonal basis may be better conditioned than that of the power series form when finding polynomial roots. However when transforming the GCD problem into a linear algebra problem requires the determination of the matrix rank and solving corresponding systems of linear equations. As such, conditioning issues may arise in certain types of inputs. In this report preliminary results using the Gauss elimination method with partial pivoting and the QR decomposition algorithm for solving systems of linear equations are implemented to find the GCD of certain class of polynomials and the results presented.