Graphics Programs Reference
In-Depth Information
8.
Use Neville's method to determine the equation of the quadraticthat passes
through the points
x
−
1
1
3
y
17
−
7
−
15
9.
The density of air
ρ
varies with elevation
h
in the following manner:
h
(km)
0
3
6
(kg/m
3
)
ρ
1
.
225
0
.
905
0
.
652
ρ
(
h
) as a quadraticfunctionusing Lagrange's method.
10.Determine the naturalcubicsplinethat passes through the datapoints
Express
x
0
1
2
y
0
2
1
Note that the interpolantconsists of twocubics, one valid in 0
≤
x
≤
1
,
the other
in 1
≤
x
≤
2
.
Verify that these cubics have the same first and second derivatives
=
at
x
1.
11.
Given the datapoints
x
1
2
3
4
5
y
13
15
12
9
13
4.
12. Compute the zero of the function
y
(
x
)from the following data:
determine the naturalcubicspline interpolant at
x
=
3
.
x
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
y
1
.
150
0
.
855
0
.
377
−
0
.
266
−
1
.
049
Use inverse interpolationwith the naturalcubicspline.
Hint
:reorder the data so
that the values of
y
are in ascending order.
13. Solve Example 3.6 with a cubicsplinethathasconstant second derivatives within
its first and last segments (the end segments are parabolic). The end conditions
for thisspline are
k
1
=
k
2
and
k
n
−
1
=
k
n
.
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