Graphics Programs Reference
In-Depth Information
2. Find the zeroof
y
(
x
)from the following data:
.
.
.
x
0
0
5
1
1
5
2
2
5
3
y
1
.
8421
2
.
4694
2
.
4921
1
.
9047
0
.
8509
−
0
.
4112
−
1
.
5727
Use Lagrange's interpolation over (a)three; and (b)four nearest-neighbordata
points.
Hint
:after finishing part(a), part(b)can becomputedwith arelatively
small effort.
3.
The function
y
(
x
) representedbythe datainProb. 2 has amaximumat
x
.
Compute this maximum by Neville's interpolation over four nearest-neighbor
datapoints.
=
0
.
7679
4.
Use Neville's method to compute
y
at
x
=
π/
4from the datapoints
x
0
0
.
5
1
1
.
5
2
y
−
1
.
00
1
.
75
4
.
00
5
.
75
7
.
00
5.
Given the data
x
0
0
.
5
1
1
.
5
2
y
−
0
.
7854
0
.
6529
1
.
7390
2
.
2071
1
.
9425
find
y
at
x
=
π/
4 and at
π/
2
.
Use the method that you consider to be most con-
venient.
6.
The points
x
−
2
1
4
−
1
3
−
4
−
−
y
1
2
59
4
24
53
lieonapolynomial. Use the divideddifference table of Newton's method to de-
termine the degree of the polynomial.
7.
Use Newton's method to find the expression for the lowest-orderpolynomialthat
fits the following points:
x
−
3
2
−
1
3
1
y
0
5
−
4
12
0
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