Graphics Programs Reference
In-Depth Information
The program should have no input apartfrom
n
. By running the program, de-
termine the largest
n
forwhich the solutionis within 6 significant figures of the
exact solution
111
T
=
x
···
(the results depend on the software and the hardware used).
16.
Write a function for the solutionphase of Choleski's decompositionmethod.
Test the functionbysolving the equations
Ax
=
b
,
where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
4
−
22
6
A
=
b
=
−
22
−
4
−
10
27
2
−
4
11
Use the function
choleski
for the decompositionphase.
17.
Determine the coefficients of the polynomial
y
=
a
0
+
a
1
x
+
a
2
x
2
+
a
3
x
3
that
.
18.
Determine the 4th degree polynomial
y
(
x
)that passes through the points
(0
passes through the points (0
,
10), (1
,
35), (3
,
31) and (4
,
2)
,
−
1), (1
,
1), (3
,
3), (5
,
2) and (6
,
−
2)
.
19.
Find the 4th degree polynomial
y
(
x
)that passes through the points (0
,
1),
(0
.
75
,
−
0
.
25) and (1
,
1), and haszerocurvature at(0
,
1) and (1
,
1)
.
20.
Solve the equations
Ax
=
b
,
where
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
.
.
−
.
.
.
3
50 2
77
0
76
1
80
7
31
−
1
.
80 2
.
68
3
.
44
−
0
.
09
4
.
23
A
=
b
=
0
.
27 5
.
076
.
90
1
.
61
13
.
85
1
.
71 5
.
452
.
68
1
.
71
11
.
55
By computing
|
A
|
and
Ax
commenton the accuracy of the solution.
2.4
Symmetric and Banded Coefficient Matrices
Introduction
Engineering problems often lead to coefficient matrices that are
sparsely populated
,
meaning that most elements of the matrix arezero. If all the nonzeroterms areclus-
teredabout the leading diagonal, then the matrix issaid to be
banded
.Anexample of
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