Graphics Programs Reference
In-Depth Information
P(1:n,k+1:n) = P(1:n,k+1:n) - v*u';
end
EXAMPLE 9.7
Transform the matrix
⎡
⎣
⎤
⎦
72 3
1
28 5 1
3512 9
−
A
=
−
11 9 7
into tridiagonalform using Householderreduction.
Solution
Reduce the first row and column:
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
851
5129
197
2
3
A
=
x
=
k
= |
x
| =
3
.
7417
−
1
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
k
+
x
1
x
2
x
3
5
.
7417
3
1
2
|
2
u
=
H
=
u
|
=
21
.
484
−
1
⎡
⎣
⎤
⎦
32
.
967 17 225
−
5
.
7417
uu
T
=
17
.
225
9
−
3
−
.
−
5
7417
3
1
⎡
⎣
⎤
⎦
−
0
.
53450
−
0
.
80176 0
.
26725
uu
T
H
Q
=
I
−
=
−
0
.
80176
0
.
58108 0
.
13964
0
.
26725
0
.
139640
.
95345
⎡
⎣
⎤
⎦
10
.
642
−
0
.
1388
−
9
.
1294
QA
Q
=
−
0
.
1388
5
.
9087
4
.
8429
−
9
.
12944
.
8429
10
.
4480
⎡
⎣
⎤
⎦
−
.
7
3
7417
0
0
A
11
(
Qx
)
T
−
3
.
7417
10
.
642
−
0
.
1388
−
9
.
1294
A
←
=
QA
Q
Qx
0
−
0
.
1388
5
.
9087
4
.
8429
0
−
9
.
12944
.
8429
10
.
4480
0
T
.
In the last stepwe used the formula
Qx
=
−
k
0
···
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