Coarse-graining and reconstruction for Markov matrices
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2891 | |
dc.contributor.author | Stephan, Artur | |
dc.date.accessioned | 2022-07-05T14:28:48Z | |
dc.date.available | 2022-07-05T14:28:48Z | |
dc.date.issued | 2021 | |
dc.description.abstract | We present a coarse-graining (or model order reduction) procedure for stochastic matrices by clustering. The method is consistent with the natural structure of Markov theory, preserving positivity and mass, and does not rely on any tools from Hilbert space theory. The reconstruction is provided by a generalized Penrose-Moore inverse of the coarse-graining operator incorporating the inhomogeneous invariant measure of the Markov matrix. As we show, the method provides coarse-graining and reconstruction also on the level of tensor spaces, which is consistent with the notion of an incidence matrix and quotient graphs, and, moreover, allows to coarse-grain and reconstruct fluxes. Furthermore, we investigate the connection with functional inequalities and Poincaré-type constants. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9609 | |
dc.identifier.uri | https://doi.org/10.34657/8647 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2891 | |
dc.relation.issn | 2198-5855 | |
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 | |
dc.subject.other | Model-order reduction | eng |
dc.subject.other | stochastic matrix | eng |
dc.subject.other | Markov matrix | eng |
dc.subject.other | generalized Penrose--Moore inverse | eng |
dc.subject.other | coarse-graining and reconstruction | eng |
dc.subject.other | clustering | eng |
dc.subject.other | flux reconstruction | eng |
dc.subject.other | discrete functional inequalities | eng |
dc.subject.other | discrete Dirichlet forms | eng |
dc.subject.other | Poincaré-type constants | eng |
dc.title | Coarse-graining and reconstruction for Markov matrices | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 17 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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