The eigenvalue spectrum of a class of nonsymmetric preconditioned matrices arising in time-dependent partial differential equations is analyzed and discussed. The matrices generated by the underlying numerical integrators are small rank perturbations of block Toeplitz matrices; circulant-like preconditioners based on the former are considered. The eigenvalue distribution of the preconditioned matrix influences often crucially the convergence of Krylov iterative accelerators.
Spectral analysis of nonsymmetric quasi-Toeplitz matrices with applications to preconditioned multistep formulas
DI BENEDETTO, FABIO
2007-01-01
Abstract
The eigenvalue spectrum of a class of nonsymmetric preconditioned matrices arising in time-dependent partial differential equations is analyzed and discussed. The matrices generated by the underlying numerical integrators are small rank perturbations of block Toeplitz matrices; circulant-like preconditioners based on the former are considered. The eigenvalue distribution of the preconditioned matrix influences often crucially the convergence of Krylov iterative accelerators.
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