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An alternative way of solving large Lyapunov equations
Author(s) -
Eppler André K.,
Bollhöfer Matthias
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010266
Subject(s) - krylov subspace , preconditioner , convergence (economics) , lyapunov function , rank (graph theory) , generalized minimal residual method , computer science , truncation (statistics) , mathematics , passivity , scale (ratio) , mathematical optimization , iterative method , engineering , combinatorics , nonlinear system , quantum mechanics , economics , economic growth , physics , machine learning , electrical engineering
System reduction has become an essential tool in simulating large electrical circuits. Among such methods balanced truncation is in particular popular since it preserves properties like passivity of the underlying descriptor system. One of the main tasks therein consists of solving large scale Lyapunov equations efficiently. In this setting one is looking for a symmetric low rank solution. For this purpose we discuss Krylov‐subspace methods such as the G eneral‐ M inimal‐ R esidual method. To speed up convergence the method is combined with the L ow R ank C holesky‐ F actor‐ A lternating‐ D irect‐Implicit‐ I teration as a structure preserving preconditioner. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)