ABSTRACT
As a general rule, larger values of wopt are associated with larger systems of equations. In Section 9.6, Eqs. (9.51) and (9.52), a procedure is described for estimating wopt for the system of equations obtained when solving the Laplace equation in a rectangular domain with Dirichlet boundary conditions. In general, one must resort to numerical experimentation to determine wopt ' In spite of this inconvenience, it is almost always worthwhile to search for a near optimum value of W if a system of equations is to be solved many times. In some problems, the computation time can be reduced by factors as large as 10 to 50. For serious calculations with a large number of equations, the potential is too great to ignore.
Example 1.23. The SOR method.
