Civil Engineering Reference
In-Depth Information
+
…
+
ax ax ax ax
ax ax ax ax
ax
+
+
=
0
0
11 1
122 13
3
1
nn
+
…
+
+
+
=
21 1
222 23
3
2
nn
+
…
+
+
ax ax ax
+
=
0
31
1
322 33
3
3
nn
+
…
+
ax a
+
xax
+
a x
=
0
n
11
n
22 33
n
nn
n
This can be written in matrix form, [
A
][
x
]=[0], as follows:
Table 2.18.
Example 2.14 Gauss-Seidel iteration method
x
1
=
5.000
∆x
1
=
5.000
x
2
=
5.300
∆x
2
=
5.300
x
3
=
5.140
∆x
3
=
5.140
x
4
=
5.456
∆x
4
=
5.456
x
1
=
2.896
∆x
1
=
-2.104
x
2
=
4.116
∆x
2
=
-1.184
x
3
=
5.042
∆x
3
=
-0.098
x
4
=
6.005
∆x
4
=
0.549
x
1
=
2.980
∆x
1
=
0.083
x
2
=
3.999
∆x
2
=
-0.117
x
3
=
5.002
∆x
3
=
-0.040
x
4
=
6.004
∆x
4
=
-0.001
<epsilon
x
1
=
2.999
∆x
1
=
0.020
x
2
=
3.999
∆x
2
=
0.000
<epsilon
x
3
=
5.000
∆x
3
=
-0.002
<epsilon
x
4
=
6.000
∆x
4
=
-0.004
<epsilon
x
1
=
3.000
∆x
1
=
0.001
<epsilon
x
2
=
4.000
∆x
2
=
0.001
<epsilon
x
3
=
5.000
∆x
3
=
0.000
<epsilon
x
4
=
6.000
∆x
4
=
0.000
<epsilon
