The perturbation bound for the solution of the Lyapunov equation. (English) Zbl 1146.15005
The author presents a new first order error bound for the Lyapunov equation \(AX +XA^*= - GG^*\) where \(A\) is perturbed to \(A+ \Delta A\). The new bound depends on the structure of \(G\) and can sometimes be sharper than the classical error bounds.
Reviewer: Stef Graillat (Paris)
MSC:
15A24 | Matrix equations and identities |
15A45 | Miscellaneous inequalities involving matrices |
65F30 | Other matrix algorithms (MSC2010) |