Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2339 | |
dc.contributor.author | Redmann, Martin | |
dc.contributor.author | Freitag, Melina A. | |
dc.date.accessioned | 2016-12-20T22:47:22Z | |
dc.date.available | 2019-06-28T08:02:13Z | |
dc.date.issued | 2016 | |
dc.description.abstract | When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2043 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1769 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Model order reduction | eng |
dc.subject.other | balanced truncation | eng |
dc.subject.other | singular perturbation approximation | eng |
dc.subject.other | stochastic systems | eng |
dc.subject.other | Lévy process | eng |
dc.subject.other | Gramians | eng |
dc.subject.other | Lyapunov equations | eng |
dc.title | Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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