Author(s) :
Tatjana Stykel
Preprint series :
Linear Algebra Appl., 349(1-3), 2002, pp. 155-185
MSC 2000
- 15A24 Matrix equations and identities
-
65F35 Matrix norms, conditioning, scaling
Abstract :
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.
Keywords :
generalized Lyapunov equations, matrix pencils, deflating subspaces, spectral projections, perturbation theory, condition numbers