Abstract
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.
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