Graphics Programs Reference
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11.
Use the Gauss-Seidel method to solve
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
−
25 9
71 1
x
1
x
2
x
3
1
6
−
37
−
1
−
26
12. Solve the following equations with the Gauss-Seidel method:
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
12
−
231
x
1
x
2
x
3
x
4
0
0
20
0
−
2 56
−
3
−
16 0
4
0
−
329
13.
Use the Gauss-Seidel methodwith relaxation to solve
Ax
=
b
,
where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
4
−
1
00
15
10
10
10
−
1
4
−
1
0
A
=
b
=
0
−
1
4
−
1
−
00
13
Take
x
i
=
b
i
/
A
ii
as the starting vector and use
ω
=
1
.
1 for the relaxation factor.
14.Solve the equations
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
2
−
1
0
x
1
x
2
x
3
1
1
1
−
12
−
1
0
−
11
by the conjugate gradient method. Start with
x
=
0
.
15.
Use the conjugate gradient method to solve
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
3
0
−
1
x
1
x
2
x
3
4
10
−
04
2
−
1
−
25
−
10
0
.
16.
Solve the simultaneousequations
Ax
starting with
x
=
=
=
b
and
Bx
b
by the Gauss-Seidel
methodwith relaxation, where
10
810
T
b
=
−
810 10
−
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