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Abstract: In this paper we will discuss some optimality results for the approximation of large-scale matrix equations. In particular this will include the special case of Lyapunov and Sylvester equations respectively. We show a relation between the iterative rational Krylov algorithm and a Riemannian optimization method which recently has been shown to locally minimize a certain energy norm of the underlying Lyapunov operator. Moreover we extend the results for a more general setting leading to a slight modification of IRKA. By means of some numerical test examples we will show the efficiency of the proposed methods. |
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