QR Factoring to Compute the GCD of Univariate Approximate Polynomials

An algorithm based on QR factoring of the Sylvester matrix, using its structure, is presented for computing the GCD of univariate approximate polynomials over R(x) or C(x). Some mathematical difficulty owing to distribution of common roots are discussed. The generalized fast and stable Schur algorithm is applied to the Sylvester matrix to facilitate the computation.