Download Dimension Reduction of Large-Scale Systems: Proceedings of a by Peter Benner, Volker Mehrmann, Danny C. Sorensen PDF

By Peter Benner, Volker Mehrmann, Danny C. Sorensen

In the earlier a long time, version aid has turn into an ubiquitous instrument in research and simulation of dynamical structures, keep watch over layout, circuit simulation, structural dynamics, CFD, and lots of different disciplines facing complicated actual types. the purpose of this booklet is to survey the most profitable version relief tools in instructional type articles and to offer benchmark difficulties from a number of program components for checking out and evaluating present and new algorithms. because the mentioned equipment have usually been constructed in parallel in disconnected program parts, the goal of the mini-workshop in Oberwolfach and its lawsuits is to make those rules on hand to researchers and practitioners from these kinds of varied disciplines.

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In: Proc. 2000 IEEE Intl. Symp. CACSD, Anchorage, Alaska, USA, September 25–27, 2000, pages 255–260. IEEE Press, Piscataway, NJ (2000). : Efficient numerical algorithms for balanced stochastic truncation. Int. J. Appl. Math. Comp. , 11:5, 1123–1150 (2001). : Parallel algorithms for model reduction of discrete-time systems. Int. J. Syst. , 34:5, 319–333 (2003). : State-space truncation methods for parallel model reduction of large-scale systems. , 29, 1701–1722 (2003). : Computing optimal Hankel norm approximations of large-scale systems.

Com. Nastran. : Design and Analysis of Control Systems. CRC Press, Boca Raton, FL (1999). : Model Reduction for Control System Design. Communications and Control Engineering Series. SpringerVerlag, London, UK (2001). : Balanced parametrizations of classes of linear systems. SIAM J. Cont. , 29, 1251–1287 (1991). : A cyclic low rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. , 21:4, 1401–1418 (2000). : Linear model reduction and solution of the algebraic Riccati equation by use of the sign function.

38) with F := A − BW E −1 C. Here, XW is symmetric positive (semi-)definite and thus admits a decomposition XW = RT R. If a reduced-order model is computed from an SVD of SRT as in balanced truncation, then the reducedˆ B, ˆ C, ˆ D) ˆ is stochastically balanced. That is, the Gramians order model (A, ˆ ˆ Wc , XW of the reduced-order model satisfy ˆ c = diag (σ1 , . . 39) where 1 = σ1 ≥ σ2 ≥ . . ≥ σr > 0. 40) ˆ From that we obtain where G∆r = G − G. n ˆ ∞ 1 + σj G−G ≤ − 1. 41) Therefore, BST is also a member of the class of relative error methods which aim at minimizing ∆r for some system norm.

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