APPROXIMATE SOLUTION OF LARGE SPARSE LYAPUNOV EQUATIONS

This note describes a simple method for efficiently estimating the dominant eigenvalues and eigenvectors of the solution to a Lyapunov equation, without first solving the equation explicitly. The method is based on the power method and matrix-vector multiplications and is particularly suitable for problems where those multiplications can be done efficiently, such as where the coefficient matrices are large and sparse or low-rank. The same idea is directly applicable to balanced-truncation order reduction of linear systems.