{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T21:50:22Z","timestamp":1791409822230,"version":"4.3.3"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100004794","name":"Centre National de la Recherche Scientifique","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004794","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution of the full-order model at some selected parameter values. The approximation obtained by Galerkin projection is the solution of a reduced dynamical system with a modified flux that takes into account the time dependency of the reduced spaces. An a posteriori error estimate is derived, and a greedy algorithm using this error estimate is proposed for the adaptive selection of parameter values. The resulting method can be interpreted as a dynamical low-rank approximation method with a subspace point of view and a uniform control of the error over the parameter set.<\/jats:p>","DOI":"10.1137\/16m1071493","type":"journal-article","created":{"date-parts":[[2017,8,31]],"date-time":"2017-08-31T14:28:30Z","timestamp":1504189710000},"page":"A1766-A1792","source":"Crossref","is-referenced-by-count":31,"title":["Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems"],"prefix":"10.1137","volume":"39","author":[{"given":"Marie","family":"Billaud-Friess","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony","family":"Nouy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,31]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.08.006"},{"key":"atypb2","volume-title":"Comparison of Methods for Parametric Model Order Reduction of Instationary Problems, preprint","author":"Baur U.","year":"2015"},{"key":"atypb3","first-page":"67","volume":"9","author":"Bebendorf M.","year":"2014","journal-title":"MS & A. 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