ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection
Numerical Analysis
2013-12-05 v1 Systems and Control
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1312.1142,
title = {ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection},
author = {Thomas Wolf and Heiko K. F. Panzer and Boris Lohmann},
journal= {arXiv preprint arXiv:1312.1142},
year = {2013}
}
Comments
15 pages, 2 figures