Block variants of Hammarling's method for solving Lyapunov equations

This article is concerned with the efficient numerical solution of the Lyapunov equation A(T) X + XA = -C with a stable matrix A and a symmetric positive semidefinite matrix C of possibly small rank. We discuss the efficient implementation of Hammarling's method and propose among other algorithmic improvements a block variant, which is demonstrated to perform significantly better than existing implementations. An extension to the discrete-time Lyapunov equation A(T) XA - X = - C is also described.