Bounds on the trace of a solution to the Lyapunov equation with a general stable matrix

摘要

Some new estimates for the eigenvalue decay rate of the Lyapunov equation AX + XA(T) = B with a low rank right-hand side B are derived. The new bounds show that the right-hand side B can greatly influence the eigenvalue decay rate of the solution. This suggests a new choice of the ADI-parameters for the iterative solution. The advantage of these new parameters is illustrated on second order damped systems with a low rank damping matrix. (c) 2007 Elsevier B.V. All rights reserved.