ADI iteration for Lyapunov equations: A tangential approach and adaptive shift selection

作者：Wolf Thomas^*; Panzer Heiko K F; Lohmann Boris

来源：Applied Numerical Mathematics, 2016, 109: 85-95.

DOI：10.1016/j.apnum.2016.06.006

• Lyapunov equation
• Large-scale systems
• ADI iteration

A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are presented. Numerical examples emphasize the potential of the new results.

• 出版日期2016-11