ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection
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. Additiona...
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| creator | Wolf, Thomas Panzer, Heiko K. F Lohmann, Boris |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1312.1142 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.1312.1142</identifier><language>eng</language><subject>Computer Science - Systems and Control ; Mathematics - Dynamical Systems ; Mathematics - Numerical Analysis</subject><creationdate>2013-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1312.1142$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1312.1142$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Wolf, Thomas</creatorcontrib><creatorcontrib>Panzer, Heiko K. F</creatorcontrib><creatorcontrib>Lohmann, Boris</creatorcontrib><title>ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection</title><description>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
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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.</abstract><doi>10.48550/arxiv.1312.1142</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Systems and Control Mathematics - Dynamical Systems Mathematics - Numerical Analysis |
| title | ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection |
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