Multisplitting with Different Weighting Schemes
R. E. White · SIAM Journal on Matrix Analysis and Applications · 1989
Parallel algorithms generated by multisplittings are considered. A parallel algorithm may be formed, first, by concurrently executing the iteration associated with each splitting, and second, by forming a weighted sum of these computations. However, it is not imperative that the weighting be done last. Convergence results are obtained for a variety of other weighting schemes. In particular, it is shown that preweighting is in some cases more desirable than the traditional postweighting. Furthermore, we indicate how one can use a symmetric weighting scheme to obtain a good multisplitting version of the SSOR preconditioner. These algorithms are illustrated by computations done on an Alliant $\text{FX} /8$ .