UNIT-II INTERPOLATION & APPROXIMATION
[Pages:20]UNIT-II INTERPOLATION & APPROXIMATION LAGRANGE POLYNAMIAL
1. Find the polynomial
by using Lagrange's formula and hence find for
:
0
: 2
Solution :
1
2
5
3 12 147
: 0
1
2
5
: 0
3
12
147
Lagrange's interpolation formula, we have
To find
2. Using Lagrange's interpolation formula, calculate the profit in the 2000 year from the following data
1997
:
43
Solution : Given the data's are
1999 65
2001 159
2002 248
1997 : 43
1999 65
2001 159
2002 248
1
Lagrange's interpolation formula, we have
To find the profit in the year 2000
Hence the profit in the year 2000 is 100.
3. Using Lagrange's formula find from the following data.
:
0
1
3
4
5
: 0
1 81 256 625
Solution :
:
0
: 0
1
3
4
5
1
81
256
625
Lagrange's interpolation formula, we have
2
To fond
4. Find the third degree polynomial satisfying the following data
:
1
3
5
7
: 24 120 336 720
Solution :
:
1
3
5
7
: 24
120
336
720
Lagrange's interpolation formula, we have
3
5. Using Lagrange's interpolation formula find
Solution : Given the data's are
:
0
1
2
: 2
3
12
Lagrange's interpolation formula, we have
given that .
15 3587
6. Using Lagrange's polynomial fit a polynomial for the following data
Solution : 4
Lagrange's interpolation formula, we have
7. Find the missing term in the following table using Lagrange's interpolation.
:
0
: 1
1
2
3
4
3
9
-- 81
Solution :
:
0
1
2
4
: 1
3
9
81
Lagrange's interpolation formula, we have
5
DIVIDED DIFFERNCES
1. Using Newton's divided difference formula, find
given
.
Solution :
By Newton's divided difference interpolation formula
Here And
2. Find Solution :
as a polynomial in
-4
-1
1245 33
for the following data by Newton's divided difference formula
0
2
5
5
9
1335
6
-4 1245
-1
33
0
5
2
9
5
1335
By Newton's divided difference interpolation formula
Here
3. Find Solution :
by Newton's divided difference formula for the data,
4
5
7
10
11
13
48
100
294
900
1210
2028
4
48
5
100
7
294
7
10 900 11 1210 13 2028
By Newton's divided difference interpolation formula
Here
4. Find Solution :
by Newton's divided difference formula for the data,
0
1
2
4
5
1
14
15
5
6
0
1
1
14
2
15
4
5
5
6
By Newton's divided difference interpolation formula
8
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