Numerical solution of very large, sparse Lyapunov equations through approximate power iteration

The authors present an algorithm for the solution of large order (1000> lambda /sub 2/), then a special case of the approximate power iteration algorithm has at least one fixed point upsilon that is near to the dominant eigenvector u/sub 1/ of X, and that there is a small attractive region in IR/sup n/ containing both u/sub 1/ and upsilon .<>