Civil Engineering Reference
In-Depth Information
The reduced lower triangular matrix is shown in Table 2.8.
Table 2.8.
Example 2.11 Cholesky decomposition method
1
0
0
0
0
16
0
0
0
−8
L
=
1
3
0
0
−2
81
90
60
0
−108
16
24
12
−24
−2
The upper triangular matrix is found at the same time and is shown in
Table 2.9.
Table 2.9.
Example 2.11 Cholesky decomposition method
1
1
1
1
1
8
0
1
1.5
1.75
1.875
10.5
U|D
=
0
0
1
0.5
1.25
5
0
0
0
1
0.167
1.333
0
0
0
0
1
2
Finally, the solution is calculated from the [U|D] matrix using back substi-
tution and shown in Table 2.10.
Table 2.10.
Example 2.11 Cholesky decomposition method
1
2
x
=
2
1
2
2.10
ERROR EQuAtiOnS
Error equations are intended to increase the accuracy in which the roots
of simultaneous equations are determined by reducing the error due to
rounding off. Consider the set of equations as follows:
