ADI Method for Sylvester Equations
January 28, 2011
3:00 p.m.
Ren-Cang Li
Abstract
We are concerned with numerical solutions of large scale Sylvester equations AX XB=C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated that the so called Cholesky factored Alternating-Directioanl-Implicit (ADI) method with decent shift parameters can be very e_ective. In this talk we’ll present a generalization of Cholesky factored ADI for Sylvester equations. We also demonstrate that often much more accurate solutions that ADI solutions can be gotten by performing Galerkin projection via the column space and row space of the computed approximate solutions.