Krylov subspace methods for projected Lyapunov equations

Authors:
T. Stykel;V. Simoncini
Affiliations:
Institut für Mathematik, Universität Augsburg, Universitätsstraíe 14, 86159 Augsburg, Germany;Dipartimento di Matematica, Universití di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations play a fundamental role in balanced truncation model reduction of descriptor systems. We present generalizations of the extended block and global Arnoldi methods to projected Lyapunov equations and compare these methods with the alternating direction implicit method with respect to performance on different examples. A deflation strategy is also proposed to overcome possible breakdown in the recurrence.