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Approximate implicit subspace iteration with alternating directions for LTI system model reduction
Author(s) -
Zhou Yunkai,
Sorensen D. C.
Publication year - 2008
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.602
Subject(s) - mathematics , subspace topology , lti system theory , reduction (mathematics) , linear system , invariant subspace , singular value decomposition , krylov subspace , invariant (physics) , iterative method , algorithm , mathematical optimization , control theory (sociology) , computer science , linear subspace , pure mathematics , mathematical analysis , control (management) , artificial intelligence , geometry , mathematical physics
We propose an approximate implicit subspace iteration with alternating directions framework for linear time‐invariant system model reduction. Within this framework, dominant eigensubspaces of the product of the system Gramians are approximated directly. This has advantage over approaches that consider the system Gramians separately. We construct two methods within the framework, one uses the QR updates and the other uses the SVD updates. Numerical results show the efficiency of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd.