In earlier papers Tyrtyshnikov [42] and the first author [14] considered the analysis of clustering properties of the spectra of specific Toeplitz preconditioned matrices obtained by means of the best known matrix algebras. Here we generalize this technique to a generic Banach algebra of matrices by devising general preconditioners related to “convergent” approximation processes [36]. Finally, as case study, we focus our attention on the Tau preconditioning by showing how and why the best matrix algebra preconditioners for symmetric Toeplitz systems can be constructed in this class.
A unifying approach to abstract matrix algebra preconditioning / F. DI BENEDETTO; SERRA CAPIZZANO S.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - STAMPA. - 82(1999), pp. 57-90.
Scheda prodotto non validato
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo
Titolo: | A unifying approach to abstract matrix algebra preconditioning |
Autori: | |
Data di pubblicazione: | 1999 |
Rivista: | |
Citazione: | A unifying approach to abstract matrix algebra preconditioning / F. DI BENEDETTO; SERRA CAPIZZANO S.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - STAMPA. - 82(1999), pp. 57-90. |
Abstract: | In earlier papers Tyrtyshnikov [42] and the first author [14] considered the analysis of clustering properties of the spectra of specific Toeplitz preconditioned matrices obtained by means of the best known matrix algebras. Here we generalize this technique to a generic Banach algebra of matrices by devising general preconditioners related to “convergent” approximation processes [36]. Finally, as case study, we focus our attention on the Tau preconditioning by showing how and why the best matrix algebra preconditioners for symmetric Toeplitz systems can be constructed in this class. |
Handle: | http://hdl.handle.net/11567/188545 |
Appare nelle tipologie: | 01.01 - Articolo su rivista |