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Acceleration of convergence

As already mentioned the convergence of the presented method seems to be very slow. To improve it we need either to have a ``better'' initial guess, and/or to accelerate the convergence by applying some form of relaxation [10]. The relaxation parameter tex2html_wrap_inline5 (specified) is used to modify the solution vector [x] at iteration i as follows:

equation416

tex2html_wrap_inline333 replaces tex2html_wrap_inline335 when determining the saw-tooth correctors.

Figure 15 shows the resulting improvement in convergence when tex2html_wrap_inline337 (over-relaxation) is used. Values of tex2html_wrap_inline5 greater than 1.7 produced oscillating results. This topic requires further attention.

  figure425
Figure 15:  The convergence rate with number of iterations for the saw-tooth method and for different values of relaxation coefficients tex2html_wrap_inline5 .



Baris Gucun
Tue Mar 4 18:15:49 CST 1997