Civil Engineering Reference
In-Depth Information
2.8
iMPROVED gAuSS-JORDAn ELiMinAtiOn
MEtHOD
In comparison to the Gauss-Jordan elimination method, the improved
Gauss-Jordan elimination method uses the same space for both the
A and B arrays. This is beneficial if the amount of space available on
the computer is limited. The algorithm for this improved method is as
follows:
a
a
a
aaaa
in
kj
′ =
kj
kk
′ =
−
′
k
= … ≠
1 2 3 except
,,
n
i
k
ij
ij
ik
kj
≤≤
+≤≤+
1
1
k
j
n
1
where,
a
′ original elements
a
new elements
i
row (
n
)
j
column (m)
k
pivotal row number
In other words, normalize the matrix then utilize partial pivoting to reduce
the matrix. However, there is no need to reduce the elements under the
pivot. Reducing up and down is easier without a need to reorder the rows.
This is how Example 2.10 is performed.
Example 2.10
Improved Gauss-Jordan elimination method
Determine the solution to the following set of equations using improved
Gaussian-Jordan elimination. Include a determinant check for
uniqueness.
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
