In this paper we propose and analyze preconditioning strategies for Hermitian indefinite linear systems by using indefinite preconditioners: under very elementary assumptions, we show that the eigenvalues are real. Moreover, in the case of multilevel Toeplitz structures, we prove distributional and localization results. These techniques used in connection with the CG, GMRES, BICGstab, and QMR algorithms allow us to solve in an optimal way the corresponding linear systems. A wide numerical experimentation confirms the efficiency of the proposed procedures.
Huckle, T., Serra Capizzano, S., TABLINO POSSIO, C. (2004). Preconditioning strategies for Hermitian indefinite Toeplitz linear systems. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 25(5), 1633-1654 [10.1137/S1064827502416332].
Preconditioning strategies for Hermitian indefinite Toeplitz linear systems
TABLINO POSSIO, CRISTINA
2004
Abstract
In this paper we propose and analyze preconditioning strategies for Hermitian indefinite linear systems by using indefinite preconditioners: under very elementary assumptions, we show that the eigenvalues are real. Moreover, in the case of multilevel Toeplitz structures, we prove distributional and localization results. These techniques used in connection with the CG, GMRES, BICGstab, and QMR algorithms allow us to solve in an optimal way the corresponding linear systems. A wide numerical experimentation confirms the efficiency of the proposed procedures.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.