Graphics Programs Reference
In-Depth Information
8.
Compute all the eigenvalues of
⎡
⎣
⎤
⎦
62000
25200
0 2740
00461
00013
A
=
9.
Find the smallest twoeigenvalues of
⎡
⎣
⎤
⎦
4
−
1
0 1
−
16
−
2 0
A
=
0
−
232
1
0
2 4
10.
Compute the three smallest eigenvalues of
⎡
⎣
⎤
⎦
−
−
7
4
3
210
−
4
8
−
4
3
−
21
3
−
4
9
−
4
3
−
2
A
=
−
23
−
4
10
−
4
3
1
−
23
−
4
11
−
4
0
1
−
23
−
4
12
and the corresponding eigenvectors.
11.
Find the twosmallest eigenvalues of the 6
×
6 Hilbert matrix
⎡
⎣
⎤
⎦
11
/
21
/
3
···
1
/
6
/
/
/
···
/
1
21
31
4
1
7
1
/
31
/
4 1
/
5
···
1
/
8
=
A
.
.
.
.
.
.
.
/
/
/
···
/
1
61
71
8
1
11
Recall thatthis matrix is ill-conditioned.
12.
Rewrite the function
eValBrackets
so that it will bracket the
m
largest
eigenvalues of a tridiagonal matrix. Use thisfunction to bracket the twolargest
eigenvalues of the Hilbert matrix in Prob. 11.
13.
u
3
u
1
u
2
k
k
k
k
m
3
m
2
m
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