\input zb-basic
\input zb-ioport
\iteman{io-port 05232932}
\itemau{Li, Bingyu; Liu, Zhuojun; Zhi, Lihong}
\itemti{A structured rank-revealing method for Sylvester matrix.}
\itemso{J. Comput. Appl. Math. 213, No. 1, 212-223 (2008).}
\itemab
A fast rank-revealing algorithm for computing the numerical rank of a Sylvester matrix is obtained by exploiting the displacement structure of Sylvester matrices. The algorithm is based on the fast Cholesky factorization of $S^TS$ or $H^TH$ and relies on the generalized Schur algorithm for matrices with displacement structure. It costs $O(r(n+m))$ flops, where $n+m$ and $r$ are the size and the numerical rank of $S$. Here $H$ is the Hankel variation of the Sylvester matrix $S$. Numerical tests show that the algorithm is valid for Sylvester matrices with low rank deficiency.
\itemrv{Liu Xinguo (Qingdao)}
\itemcc{}
\itemut{numerical rank; Sylvester matrix; displacement structure; generalized Schur algorithm; Cholesky factorization; numerical examples; rank-revealing algorithm}
\itemli{doi:10.1016/j.cam.2007.01.032}
\end