Page 227 - Excel for Scientists and Engineers: Numerical Methods

204 EXCEL: NUMERICAL METHODS

=($E$8-$C$8*C13-$D$8*D13)/$B$8
=($E$9-$B$9*B14-$D$9*D13)/$C$9

=($E$l O-$B$1 O*B14-$C$1 O*C14)/$D$IO
and, as can be seen in Figure 9-1 1, the formulas converge more rapidly to the
specified level of precision.

Figure 9-1 1. Satisfactory convergence is reached with the Gauss-Seidel method
after 15 iteration cycles.
(folder 'Chapter 09 Simultaneous Equations', workbook 'Simult Eqns II', sheet 'Gauss-Seidel 1')

You may wish to experiment with changing the values of the coefficients. In
particular, see the effect of making the diagonal elements large, or off-diagonal
elements large.

The Gauss-Seidel Method
Implemented on a Worksheet
Using Circular References
The worksheet in the preceding section can be easily modified to use
intentional circular references, as follows. After entering the starting values in
row 13 and the formulas in row 14 as before (Figure 9-11), change the cell