the end of the table and also for extrapolation to the
right of y
n
.
Example 6.17
Find the cubic polynomial y
x
which takes on the
values
y
0
=− 5, y
1
= 1, y
2
= 9, y
3
= 25,
y
4
= 55, y
5
= 105
Use the difference table to calculate y
3.2
.
Solution Constructing the difference table for the
function we have
Putting
00
1
0
2
30
1,
2
2,
3
3, .
xxxxh
xx
pp
hhh
xxh
xx
p
hh
xxxxh
petc
hh
−+−
−
=⇒==−
−−
−
==−
−−−
==−
formula (6.45) can be put in a simpler form as
fD
DD
D
D
=
== ...
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