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The coefficient matrix
is diagonally dominant as
and the inequality is strictly greater than for at least one row. Hence the solution should converge using Gauss-Seidal method.
Rewriting the equations, we get
Assuming an initial guess of
Iteration 1:
=0.50000
=4.9000
=3.0923
The absolute relative approximate error at the end of first iteration is
=67.662%
=100.000%
=67.662%
The maximum absolute relative approximate error is 100.000%
Iteration 2:
=0.14679
=3.7153
=3.8118
At the end of second iteration, the absolute relative approximate error is
=240.62%
=31.887%
=18.876%.
The maximum absolute relative approximate error is 240.62%. This is greater than the value of 67.612% we obtained in the first iteration. Is the solution diverging? No, as you conduct more iterations, the solution converges as follows.
| Iteration | a1 | 
| a2 | 
| a3 | 
|
| 0.50000 0.14679 0.74275 0.94675 0.99177 0.99919 | 67.662 240.62 80.23 21.547 4.5394 0.74260 | 4.900 3.7153 3.1644 3.0281 3.0034 3.0001 | 100.00 31.887 17.409 4.5012 0.82240 0.11000 | 3.0923 3.8118 3.9708 3.9971 4.0001 4.0001 | 67.662 18.876 4.0042 0.65798 0.07499 0.00000 |
This is close to the exact solution vectorof
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