On the Perturbation Bounds of Projected Generalized Continuous-Time Sylvester Equations

On the Perturbation Bounds of Projected Generalized Continuous-Time Sylvester Equations

A Schur Method for Solving Projected Continuous-Time Sylvester Equations

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy. Keywords—Pro...

On the numerical solution of generalized Sylvester matrix equations

‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

The Projected Generalized Sylvester Equations: Numerical Solution and Applications

In this paper we consider the numerical solution of large-scale projected generalized continuous-time and discrete-time Sylvester equations with low-rank right-hand sides. First, we present the results on the sufficient conditions for the existence, uniqueness, and analytic formula of the solutions of these equations. Second, we review the low-rank alternating direction implicit method and the ...

A Generalized HSS Iteration Method for Continuous Sylvester Equations

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the ...