Low-rank iterative methods for projected generalized Lyapunov equations. (English) Zbl 1171.65385

Summary: 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.


65F30 Other matrix algorithms (MSC2010)
65F10 Iterative numerical methods for linear systems
15A22 Matrix pencils
15A24 Matrix equations and identities
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