An iterative method for the low-rank approximate solution of a class of generalized Lyapunov equations is studied. At each iteration, a standard Lyapunov equation is solved using Galerkin projection with an extended Krylov subspace method. This Lyapunov equation is solved inexactly, thus producing a nonstationary iteration. Several theoretical and computational issues are discussed so as to make the iteration efficient. Numerical experiments indicate that this method is competitive vis-à-vis the current state-of-the-art methods, both in terms of computational times and storage needs.
Efficient low-rank solution of generalized Lyapunov equations
SIMONCINI, VALERIA;
2016
Abstract
An iterative method for the low-rank approximate solution of a class of generalized Lyapunov equations is studied. At each iteration, a standard Lyapunov equation is solved using Galerkin projection with an extended Krylov subspace method. This Lyapunov equation is solved inexactly, thus producing a nonstationary iteration. Several theoretical and computational issues are discussed so as to make the iteration efficient. Numerical experiments indicate that this method is competitive vis-à-vis the current state-of-the-art methods, both in terms of computational times and storage needs.File in questo prodotto:
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