Graphics Programs Reference
In-Depth Information
Solution
% Example 2.8 (Choleski decomposition)
A = [1.44 -0.36 5.52 0.00;
-0.36 10.33 -7.78 0.00;
5.52 -7.78 28.40 9.00;
0.00 0.00 9.00 61.00];
L = choleski(A)
Check = L*L' % Verify the result
>>L=
1.2000
0
0
0
-0.3000
3.2000
0
0
4.6000
-2.0000
1.8000
0
0
0
5.0000
6.0000
Check =
1.4400
-0.3600
5.5200
0
-0.3600
10.3300
-7.7800
0
5.5200
-7.7800
28.4000
9.0000
0
0
9.0000
61.0000
PROBLEM SET 2.1
1. By evaluating the determinant, classify the following matrices assingular, ill-
conditioned orwell-conditioned.
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
123
234
3 4 5
2
.
11
−
0
.
80 1
.
72
(a)
A
=
(b)
A
=
−
1
.
84
3
.
031
.
29
−
1
.
57
5
.
25 4
.
30
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
−
−
2
1
0
4
3
1
(c)
A
=
−
12
−
1
(d)
A
=
7
−
23
0
−
12
5
−
18
13
2.
Given the LU decomposition
A
=
LU
,
determine
A
and
|
A
|
.
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
1 00
110
15
12 4
0 321
00 0
(a)
L
=
U
=
/
31
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
00
2
−
11
(b)
L
=
−
110
1
U
=
0
3
001
1
−
−
31
Search WWH ::
Custom Search