Volume 30, pp. 187-202, 2008.

Low-rank iterative methods for projected generalized Lyapunov equations

Tatjana Stykel

Abstract

We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximations to the solution of projected generalized Lyapunov equations with low-rank symmetric, positive semidefinite right-hand side. Numerical examples are presented.

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Key words

projected generalized Lyapunov equations, alternating direction implicit method, Smith method, low-rank approximation

AMS subject classifications

65F10, 65F30, 15A22, 15A24

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