The Mechanization of the Comrade Matrix Approach in Determining the GCD of Orthogonal Polynomials

Abstract

This paper revisits the comrade matrix approach in finding the greatest common divisor (GCD) of two orthogonal polynomials. The present work investigates on the applications of the QR decomposition with iterative refinement (QRIR) to solve certain systems of linear equations which is generated from the comrade matrix. Besides iterative refinement, an alternative approach of improving the conditioning behavior of the coefficient matrix by normalizing its columns is also considered. As expected the results reveal that QRIR is able to improve the solutions given by QR decomposition while the normalization of the matrix entries do improves the conditioning behavior of the coefficient matrix leading to a good approximate solutions of the GCD.