A Link Between Gramian-Based Model Order Reduction and Moment Matching

Autor:	Christian Bertram, Heike Faßbender
Rok vydání:	2021
Předmět:	Model order reduction Dynamical systems theory Applied mathematics Time step Linear subspace Eigenvalues and eigenvectors Mathematics::Numerical Analysis Gramian matrix Mathematics Quadrature (mathematics)
Zdroj:	Model Reduction of Complex Dynamical Systems ISBN: 9783030729820
DOI:	10.1007/978-3-030-72983-7_6
Popis:	We analyze a family of Runge-Kutta-based quadrature algorithms for the approximation of the Gramians of linear time-invariant dynamical systems. The approximated Gramians are used to obtain an approximate balancing transformation similar to the approach used in balanced POD. It is shown that hereby rational interpolation is performed, as the approximants span certain Krylov subspaces. The expansion points are mainly determined by the time step sizes and the eigenvalues of the matrices given by the Butcher tableaus.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5156c890d46b3f99b2ea8015e32cdc5e https://doi.org/10.1007/978-3-030-72983-7_6 Zobrazit plný text záznamu