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.
2016
Shank, Stephen D.; Simoncini, Valeria; Szyld, Daniel B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/586009
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