A structured rank-revealing method for Sylvester matrix

We propose a fast algorithm for computing the numeric ranks of Sylvester matrices. Let S denote the Sylvester matrix and H denote the Hankel-like-Sylvester matrix. The algorithm is based on a fast Cholesky factorization of S T S or H T H and relies on a stabilized version of the generalized Schur algorithm for matrices with displacement structure. All computations can be done in O ( r ( n + m ) ) , where n + m and r denote the size and the numerical rank of the Sylvester matrix, respectively.