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.
Keywords: algorithms ; performance ; Lyapunov equation ; numerical solution ; block algorithm ; Multishift Qr Algorithm ; Numerical-Solution ; Triangular Systems ; Matrix Equations ; Part Ii ; Sylvester ; Performance
Record created on 2011-05-05, modified on 2016-08-09