Avoiding complex arithmetic in the low-rank ADI method efficiently

We present a new reformulation of the low-rank ADI method for solving large-scale Lyapunov equations which uses only real arithmetic operation and storage in the presence of complex shift parameters. This makes the method applicable on computing environments where complex computations and storage are not supported or not efficiently available. For generalized Lyapunov equations it is significantly more efficient than the older completely real formulation of the low-rank ADI as confirmed by numerical examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)