Chahlaoui, Younès (2011) Two efficient SVD/Krylov algorithms for model order reduction of large scale systems. Electronic Transactions On Numerical Analysis (ETNA), 38. pp. 113145. ISSN 10689613
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Abstract
We present two efficient algorithms to produce a reduced order model of a timeinvariant linear dynamical system by approximate balanced truncation. Attention is focused on the use of the structure and the iterative construction via Krylov subspaces of both controllability and observability matrices to compute lowrank approximations of the Gramians or the Hankel operator. This allows us to take advantage of any sparsity in the system matrices and indeed the cost of our two algorithms is only linear in the system dimension. Both algorithms efficiently produce good lowrank approximations (in the least square sense) of the Cholesky factor of each Gramian and the Hankel operator. The second algorithm works directly on the Hankel operator, and it has the advantage that it is independent of the chosen realization. Moreover it is also an approximate Hankel norm method. The two reduced order models produced by our methods are guaranteed to be stable and balanced. We study the convergence of our iterative algorithms and the properties of the fixed point iteration. We also discuss the stopping criteria and the choice of the reduced order.
Item Type:  Article 

Uncontrolled Keywords:  CICADA 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 93 Systems theory; control 
Depositing User:  Dr Younes Chahlaoui 
Date Deposited:  29 Jun 2011 
Last Modified:  20 Oct 2017 14:12 
URI:  http://eprints.maths.manchester.ac.uk/id/eprint/1636 
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Two efficient SVD/Krylov algorithms for model order reduction of large scale systems. (deposited 14 Jan 2010)
 Two efficient SVD/Krylov algorithms for model order reduction of large scale systems. (deposited 29 Jun 2011) [Currently Displayed]
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