Civil Engineering Reference
In-Depth Information
= …
=++…
j
234
12
,,,
,
n
−
∑
1
j
1
aa aa
=−
For
i
j
,
j
,
j
,
,
n
ij
,
ij
ik
kj
k
=
(
)
forea
ch valueofj
= …
=++…+
i
234
12 1
,,,
,
n
∑
1
i
−
a
−
a a
ij
ik
kj
k
=
a
=
For
jii
,
,
i
,
,
n
ij
,
a
(
)
ii
f
or each valueofi
Example 2.11
Cholesky decomposition method
Find the solution set to the following non-homogeneous linear algebraic
equations using Cholesky decomposition.
8
16 842144
2
xx xxx
xx x
++++=
++++=
−+−+=
1
2
3
4
5
x
x
1
2
3
4
5
xx xxx
x
1
2
3
4
5
81
27 93 44
16 842
− + −+=
−+−+=
x
x
xx
1
2
3
4
5
xx x
x
x
8
1
2
3
4
5
l
l
00
0
1
01
00 1
uud
ud
d
aaac
aaac
aaac
11
12
13
1
11
12
13
1
l
=
21
22
23
2
21
22
23
2
l
l
l
31
32
33
3
31
32
33
3
The matrix in augmented form is shown in Table 2.7.
Table 2.7.
Example 2.11 Cholesky decomposition
method
1
1
1
1
1
8
16
8
4
2
1
44
A
=
1
1
1
2
−1
−1
81
9
1
44
−27
−3
16
4
1
8
−8
−2
