Graphics Programs Reference
In-Depth Information
Reduce the second row and column:
5
.
9087
4
.
8429
−
0
.
1388
A
=
x
=
k
=−|
x
| =−
9
.
1305
4
.
8429 10
.
4480
−
9
.
1294
where the negativesign on
k
was determinedbythe sign of
x
1
.
k
+
x
1
x
2
−
9
.
2693
1
2
|
2
u
=
=
H
=
u
|
=
84
.
633
−
9
.
1294
85
.
920 84
.
623
uu
T
=
.
.
84
623 83
346
0
uu
T
H
.
01521
−
0
.
99988
Q
=
I
−
=
−
0
.
99988
0
.
01521
10
.
5944
.
772
QA
Q
=
4
.
772 5
.
762
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
7
−
3
.
742
0
0
A
11
A
12
0
T
A
21
A
22
(
Qx
)
T
0 x A
Q
−
3
.
742 0
.
6429
.
131
0
A
←
0
9
.
131 10
.
5944
.
772
.
.
0
0
4
772 5
762
EXAMPLE 9.8
Use the function
householder
to tridiagonalize the matrix in Example 9.7; also de-
termine the transformationmatrix
P
.
Solution
% Example 9.8 (Householder reduction)
A=[7 2 3-1;
2851;
3 5 12 9;
-1 1 9 7];
A = householder(A);
d = diag(A)'
c = diag(A,1)'
P = householderP(A)
The results of running the above program are:
>>d=
7.0000
10.6429
10.5942
5.7629
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