Block-Toeplitz preconditioning for static and dynamic linear systems Original Research Article

Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (yʹ = Qy + g(t)) type are analyzed. A new splitting Q = M − N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.