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^TS$S^{\mathrm{T}}S$ or H^TH$H^{\mathrm{T}}H$ 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))$\mathrm{O}(r(n+m))$, where n+m$n+m$ and r denote the size and the numerical rank of the Sylvester matrix, respectively.