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In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new approach projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in A and A^-1. The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the competitiveness of the new method, compared to a state-of-the-art approach based on the factorized alternating direction implicit iteration.
Valeria Simoncini (Mon,) studied this question.
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