Matrix analysis
On the Stability of the Bareiss and Related Toeplitz Factorization Algorithms
SIAM Journal on Matrix Analysis and Applications
Displacement structure: theory and applications
SIAM Review
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Stabilizing the Generalized Schur Algorithm
SIAM Journal on Matrix Analysis and Applications
A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Polynomials and Linear Control Systems
Polynomials and Linear Control Systems
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
Blind image deconvolution via fast approximate GCD
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
| Hi-index | 7.29 |
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 or H^TH 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.