Sparce matrix solution of the Lyapunov equation

Abstract

It is well known [2, 3] that the nth order Lyapunov equation, AP+PA'=-Q, can be expanded to a n(n+1)/2 order linear vector equation and then solved using conventional linear equation methods. The purpose of this short paper is to present recent work on the sparceness of the resulting equation and the computational advantage of that sparceness, for large n.