Numerical solution of the Lyapunov equation by approximate power iteration
The numerical solution of the Lyapunov equation has been addressed for several decades. In some applications, one is frequently interested in computing only the dominant invariant subspace of the symmetric positive definite solution \(X\) rather than the matrix \(X\) itself. This paper presents an approximate power iteration algorithm to solve this problem. Numerical experiments indicate that, if the matrix \(X\) admits a good low-rank solution, then the solver proposed in this paper provides indeed an orthogonal basis of a subspace which closely approximates the dominant \(X\)-invariant subspaces of corresponding dimension. A convergence analysis is also presented.
scientific article; zbMATH DE number 871267
scientific article