Efficient Implementations of Certain Iterative Methods
James M. Ortega · SIAM Journal on Scientific and Statistical Computing · 1988
We compare procedures given by Bank and Douglas [Appl. Numer. Math., 1 (1985), pp. 489–492], Conrad and Wallach [Numer. Math., 27 (1979), pp. 371–372], and Eisenstat [SIAMJ. Sci. Statist. Comput., 2 (1981), pp. 1–4] for reducing computation in certain preconditioned conjugate gradient or other iterative methods, for example, the SSOR iteration and SSOR preconditioning. The procedures are first formulated in a common framework and it is shown that, although different, they are more closely related than it first appears. Operation counts are given which show that the Bank–Douglas and Eisenstat procedures are essentially comparable, and are better than the Conrad–Wallach procedure for preconditioning.