Notes on Use

If selected, scaling and unscaling the matrix may introduce small changes in the coefficient matrix and the right hand side vector RHS due to round-off errors in the computer arithmetic. Also, many preconditioners will attempt to rearrange COEF and JCOEF to enhance vectorization. Thus, the COEF and JCOEF arrays on output will be equivalent to but will not, in general, be identical to the input arrays. For the Successive Overrelaxation (SOR) method, it is sometimes possible to find red-black or multicolor orderings of the equations for which the method has the same rate of convergence as for the natural ordering. Thus, a red-black, line red-black, or multicolor ordering may be preferable to the natural ordering since greater vectorizability is possible. The SSOR, IC, MIC, and block factorization methods, however, have better convergence rates with natural ordering than with multi-color orderings. Since these methods vectorize better with a multicolor ordering, there is a tradeoff between fewer expensive iterations and a greater number of cheap iterations. Thus, there might be ranges of problem sizes when one approach may be better than the other. This comment also applies when comparing two different preconditioners with different convergence rates such as Jacobi and MIC. For small N, Jacobi may be preferable to the more sophisticated MIC method because of its vectorizability and the relatively small difference in the number of iterations. For larger N, the difference in number of iterations will outweigh the difference in time per iteration.