Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation (Articolo in rivista)

Type
Label
  • Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation (Articolo in rivista) (literal)
Anno
  • 2011-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1137/100813257 (literal)
Alternative label
  • Druskin, V. ; Knizhnerman, L . ; Simoncini, V. (2011)
    Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation
    in SIAM journal on numerical analysis (Print); Society for Industrial and Applied Mathematics, Philadelphia, PA (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Druskin, V. ; Knizhnerman, L . ; Simoncini, V. (literal)
Pagina inizio
  • 1875 (literal)
Pagina fine
  • 1898 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 9 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 5 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopus (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Schlumberger Doll Res Ctr, Cambridge, MA. USA ; Schlumberger Doll Res Ctr, Moscow, Russia; Università di Bologna, Dipartimento di Matematica, Bologna; CIRSA, Ravenna. (literal)
Titolo
  • Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation (literal)
Abstract
  • For large scale problems, an effective approach for solving the algebraic Lyapunov equation consists of projecting the problem onto a significantly smaller space and then solving the reduced order matrix equation. Although Krylov subspaces have been used for a long time, only more recent developments have shown that rational Krylov subspaces can be a competitive alternative to the classical and very popular alternating direction implicit (ADI) recurrence. In this paper we develop a convergence analysis of the rational Krylov subspace method (RKSM) based on the Kronecker product formulation and on potential theory. Moreover, we propose new enlightening relations between this approach and the ADI method. Our results provide solid theoretical ground for recent numerical evidence of the superiority of RKSM over ADI when the involved parameters cannot be computed optimally, as is the case in many practical application problems. (literal)
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