Perturbation analysis of the mixed-type Lyapunov equation

This paper concerns the mixed-type Lyapunov equation where and are complex matrices and the conjugate transpose of a matrix A perturbation bound for the solution to this matrix equation is derived, an explicit expression of the condition number is obtained, and the backward error of an approximate solution is evaluated by using the techniques developed in Sun (Linear Algebra Appl 259:183-208, 1997), Sun and Xu (Linear Algebra Appl 362:211-228, 2003). The results are illustrated by using some numerical examples. ? 2011 Springer Science+Business Media B.V.EI