Geodesic
Frequency analysis of preconditioned waveform relaxation iterations
Applicationes Mathematicae, Tome 26 (1999) no. 2, pp. 229-242.

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The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting from semi-discretization of the heat equation in one and two dimensions. This theory and some heuristic arguments predict that preconditioning is most effective for the first few iterations.
DOI : 10.4064/am-26-2-229-242
Keywords: error analysis, waveform relaxation, convergence, preconditioning, splitting

Andrzej Augustynowicz 1 ; Zdzisław Jackiewicz 1

1 
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Andrzej Augustynowicz; Zdzisław Jackiewicz. Frequency analysis of preconditioned waveform relaxation iterations. Applicationes Mathematicae, Tome 26 (1999) no. 2, pp. 229-242. doi : 10.4064/am-26-2-229-242. http://geodesic.mathdoc.fr/articles/10.4064/am-26-2-229-242/

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