Media type: E-Article Title: Fast Low‐Rank Empirical Cross Gramians Contributor: Himpe, Christian; Leibner, Tobias; Rave, Stephan; Saak, Jens imprint: Wiley, 2017 Published in: PAMM Language: English DOI: 10.1002/pamm.201710388 ISSN: 1617-7061 Keywords: General Medicine Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>The cross Gramian matrix encodes the input‐output coherence of linear control systems and is used in projection‐based model reduction. The empirical cross Gramian is a data‐driven variant of the cross Gramian which also extends to nonlinear systems. A drawback of the empirical cross Gramian for large‐scale systems is its full order and dense structure; yet, it may be computed column‐wise. Using the hierarchical approximate proper orthogonal decomposition (HAPOD), this partial computability can be exploited to obtain a truncated projection for model order reduction without assembling a full cross Gramian. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)</jats:p>