Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples illustrate that the new preconditioners so obtained can give faster convergence than available preconditioners based on circulant and generalized circulant matrices. © 2013 IMACS.
A note on superoptimal generalized circulant preconditioners / Noschese, Silvia; Lothar, Reichel. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - STAMPA. - 75:(2014), pp. 188-195. [10.1016/j.apnum.2013.09.002]
A note on superoptimal generalized circulant preconditioners
NOSCHESE, Silvia;
2014
Abstract
Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples illustrate that the new preconditioners so obtained can give faster convergence than available preconditioners based on circulant and generalized circulant matrices. © 2013 IMACS.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
