Contents
>> Applied Mathematics
>> Numerical Methods
>> Interpolation of Functions
>> Example
|
Interpolation of functions - Example
Example
[1]
The table of values of full elliptic integral
is given; find
К
(78º 30’).
Values of full elliptic integral K
(
α
)
|
α
|
K
(
α
)
|
ΔK
|
Δ
2
K
|
Δ
3
K
|
Δ
4
K
|
Δ
5
K
|
Δ
6
K
|
|
75º
|
2.76806
|
|
|
|
|
|
|
|
|
|
6461
|
|
|
|
|
|
|
76º
|
2.83267
|
|
528
|
|
|
|
|
|
|
|
6989
|
|
84
|
|
|
|
|
77º
|
2.90256
|
|
612
|
|
19
|
|
|
|
|
|
7601
|
|
103
|
|
13
|
|
|
78º
|
2.97857
|
|
715
|
|
32
|
|
– 5
|
|
|
|
8316
|
|
135
|
|
8
|
|
|
79º
|
3.06173
|
|
850
|
|
40
|
|
18
|
|
|
|
9166
|
|
175
|
|
26
|
|
|
80º
|
3.15339
|
|
1025
|
|
66
|
|
– 1
|
|
|
|
10191
|
|
241
|
|
25
|
|
|
81º
|
3.25530
|
|
1266
|
|
91
|
|
43
|
|
|
|
11457
|
|
332
|
|
68
|
|
|
82º
|
3.36987
|
|
1598
|
|
159
|
|
|
|
|
|
13055
|
|
491
|
|
|
|
|
83º
|
3.50042
|
|
2089
|
|
|
|
|
|
|
|
15144
|
|
|
|
|
|
|
84º
|
3.65186
|
|
|
|
|
|
|
S o l u t i o n . According to data of the table it is accepted
х
0
= 78º ;
h
=1º ;
х
= 78º 30’, from here
q
= 0.5. Being limited to differences of the fifth order, from Stirling’s interpolation formula we have:
|