Chapter 17 - The Search for Omega

Abstract

For the effective use of iterative algorithms for solving large sparse linear systems it is often necessary to select certain iteration parameters. Examples of iteration parameters are the relaxation factor omega for the SOR and SSOR methods, and the largest and smallest eigenvalues of the matrix for a basic iterative method when Chebyshev acceleration is used to speed up the convergence. For many iterative algorithms the performance is extremely sensitive to the choice of iteration parameters. Moreover, uncertainty as to how to choose iteration parameters has often, in the past, tended to discourage the use of iterative methods, as opposed to direct methods, for certain classes of problems.