A Reformulated Low‐Rank ADI Iteration with Explicit Residual Factors

Based on our recent findings [1, 2] regarding the low‐rank ADI iteration for large‐scale Lyapunov equations, we propose a mathematically equivalent formulation of the LR‐ADI whose iteration is directly connected to low rank factors of the Lyapunov residual. If complex shift parameters occur and are handled efficiently [1], this reformulation is slightly more efficient from a computational point of view, since it guarantees that the right hand sides of all linear systems that need to be solved are real. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)