Graphics Programs Reference
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=
10.Solve the equations AX
B by Doolittle's decompositionmethod, where
4
3
6
1 0
0 1
00
A
=
B
=
8
3 0
4
12
10
11. Solve the equations Ax
=
b by Choleski's decompositionmethod, where
111
122
123
1
A
=
b
=
3
/
2
3
12. Solve the equations
=
4
2
3
x 1
x 2
x 3
1
.
1
0
12
4
10
16
28
18
2
.
3
by Doolittle's decompositionmethod.
13. Determine L that results fromCholeski's decomposition of the diagonal matrix
α 1
00
···
0
α 2
0
···
A
=
α 3
···
00
.
.
.
. . .
14. Modify the function gauss so that it will work with m constant vectors. Test the
program by solving AX
=
B , where
2
1
0
1 00
0 1 0
001
A
=
B
=
12
1
0
11
15.
Awell-known example of an ill-conditionedmatrix is the Hilbert matrix
11
/
21
/
3
···
1
/
21
/
31
/
4
···
=
A
1
/
31
/
4 1
/
5
···
.
.
.
. . .
Write aprogram thatspecializes in solving the equations Ax
b by Doolittle's
decompositionmethod, where A is the Hilbert matrix of arbitrary size n
=
×
n , and
n
b i
=
A i j
j
=
1
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