Numerical solution and perturbation theory for generalized Lyapunov equations Original Research Article

We discuss the numerical solution and perturbation theory for the generalized continuous-time Lyapunov equation E*XA+A*XE=−G with a singular matrix E. If this equation has a solution, it is not unique. We generalize a Bartels–Stewart method and a Hammarling method to compute a partial solution of the generalized Lyapunov equation with a special right-hand side. A spectral condition number is introduced and perturbation bounds for such an equation are presented. Numerical examples are given.