Graphics Programs Reference
In-Depth Information
10.
Use the powermethod to compute the largest eigenvalue and the corresponding
eigenvector of the matrix
A
giveninProb. 9.
11.
Find the smallest eigenvalue and the corresponding eigenvector of the matrix
A
in Prob. 9. Use the inverse powermethod.
12.
Let
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
1
.
40
.
8 0
.
4
0
.
4
−
0
.
1
0
.
0
A
=
0
.
86
.
6 0
.
8
B
=
−
0
.
1
0
.
4
−
0
.
1
0
.
40
.
85
.
0
0
.
0
−
0
.
1
0
.
4
Bx
by the Jacobi method.
13.
Use the inverse powermethod to compute the smallest eigenvalue in Prob. 12.
14.
Use the Jacobi method to compute the eigenvalues and eigenvectorsofthe
matrix
Find the eigenvalues and eigenvectorsof
Ax
=
λ
⎡
⎣
⎤
⎦
12314 2
293521
3315 4 32
15 4 12 4 3
4 234 17 5
212358
A
=
15.
Find the eigenvalues of
Ax
=
λ
Bx
by the Jacobi method, where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
6
−
4
1
0
1
−
23
−
1
−
4
6
−
4
1
−
26
−
23
A
=
B
=
1
−
4
6
−
4
3
−
26
−
2
0
1
−
4
7
−
13
−
29
Warning
:
B
is not positive definite.
16.
u
L
x
n
2
1
The figure shows a cantileverbeamwith a superimposedfinite differencemesh. If
u
(
x
,
t
) is the lateral displacement of the beam, the differentialequation of motion
governing bending vibrations is
=−
E I
u
(4)
u
γ
where
is the mass per unitlength and
E I
is the bending rigidity. The bound-
ary conditions are
u
(0
u
(0
u
(
L
u
(
L
,
t
)
=
,
t
)
=
,
t
)
=
,
t
)
=
0.W th
u
(
x
,
t
)
=
Search WWH ::
Custom Search