The application of linear multistep formulas in boundary value form for the solutions of initial and boundary value problems requires the solutions of linear systems of which the coe cient matrices are large and sparse block-Toeplitz-like matrices. Block-circulant preconditioners applied to these linear systems are examined. Analytical formulas for the eigenvalues of these preconditioned matrices are derived. The eigenvalues are also predicted by an asymptotic analysis. Copyright ? 2004 John Wiley & Sons, Ltd.
Bertaccini, D., Wen, Y., Ng, M. (2005). The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 12(2-3), 315-325 [10.1002/nla.419].
The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form
BERTACCINI, DANIELE;
2005-01-01
Abstract
The application of linear multistep formulas in boundary value form for the solutions of initial and boundary value problems requires the solutions of linear systems of which the coe cient matrices are large and sparse block-Toeplitz-like matrices. Block-circulant preconditioners applied to these linear systems are examined. Analytical formulas for the eigenvalues of these preconditioned matrices are derived. The eigenvalues are also predicted by an asymptotic analysis. Copyright ? 2004 John Wiley & Sons, Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
