Abstract
In this paper a theoretical comparison between ART, block-ART and SIRT is presented, by expanding the iteration matrices of the methods in the relaxation parameter. If ART, block-ART and SIRT are applied with the same relaxation parameter λ≪1, the three methods are practically equivalent. Such a small parameter is required for reasons of convergence for SIRT and to a lesser extent for block-ART. ART has the advantage that the relaxation parameter can be varied over a wider range. In problems with a large amount of noise, however, strong underrelaxation has to be applied to regularize the method. This confines the superiority of ART over SIRT and block-ART to systems of equations which are mildly inconsistent. A disadvantage of ART is that it is not suited for parallel implementation.
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© 1992 Springer-Verlag Berlin Heidelberg
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van Dijke, M.C.A., van der Vorst, H.A., Viergever, M.A. (1992). On the Relation between ART, Block-ART and SIRT. In: Todd-Pokropek, A.E., Viergever, M.A. (eds) Medical Images: Formation, Handling and Evaluation. NATO ASI Series, vol 98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77888-9_16
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DOI: https://doi.org/10.1007/978-3-642-77888-9_16
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