Parallel QR processing of Generalized Sylvester matrices

In this paper, we develop a parallel QR factorization for the generalized Sylvester matrix. We also propose a significant faster evaluation of the QR applied to a modified version of the initial matrix. This decomposition reveals useful information such as the rank of the matrix and the greatest common divisor of the polynomials formed from its coefficients. We explicitly demonstrate the parallel implementation of the proposed methods and compare them with the serial ones. Numerical experiments are also presented showing the speed of the parallel algorithms.