Finite-Rank ADI Iteration for Operator Lyapunov Equations
نویسندگان
چکیده
منابع مشابه
Finite-Rank ADI Iteration for Operator Lyapunov Equations
We give an algorithmic approach to the approximative solution of operator Lyapunov equations for controllability. Motivated by the successfully applied alternating direction implicit (ADI) iteration for matrix Lyapunov equations, we consider this method for the determination of Gramian operators of infinite-dimensional control systems. In the case where the input space is finitedimensional, thi...
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Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that the ADI iteration can always be identified by a Petrov-Galerkin projection with rational block Krylov subspaces. Then a unique Krylov-projected dynamical sys...
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A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are...
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We study operator Lyapunov equations in which the innnitesimal generator is not necessarily stable; but it satisses a spectrum decomposition assumption and it has at most nitely many unstable eigenvalues. Under mild conditions; these have unique self-adjoint solutions. We give conditions under which the number of negative eigenvalues of this solution equals the number of unstable eigenvalues of...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2013
ISSN: 0363-0129,1095-7138
DOI: 10.1137/120885310