Bachelor of Computer Applications
MATOL121: Numerical Methods for Computer
Applications
Unit III: Lecture 3
NEWTON’S BACKWARD INTERPOLATION
FORMULA
Smt. D. SARALA
School of Arts Science and Humanities
SASTRA Deemed To Be University
Gregory - Newton’s backward difference formula
for equal intervals
v (v 1) 2
v (v 1) (v  2) 3
v
y(x)  yn  yn 
 yn 
 yn ...........
1!
2!
3!
where v 
x  x
h
n
Note: 1. This formula is used to interpolate (or
extrapolate) the values of y nearer to end
value of the table.
2. v lies between -1 and 0.
Practice Problems:
1.
Using
Newton’s
formula, find a
backward
interpolation
polynomial of degree 2 which
takes the values.
x : 0 1
2
3
4
5
6
7
y : 1
4
7
11
16
22
29
2
2. From the following data, find y at x = 43 and
x = 84.
x:
40
50
60
70
80
90
y : 184
204
226
250
276
304
3. Find y(32) if y(10) = 35.3, y(15) = 32.4,
y(20) = 29.2, y(25) = 26.1, y(30) = 23.2 and
y(35) = 20.5
4. Using Newton’s forward difference formula,
find the sum Sn = 13 + 23 + 33 + 43 +…..…+n3
Answers
1. Required polynomial is y(x) = (1/2)(x2+x+2).
2. y(43) = 189.79 approximately
y(84) = 286.96 approximately
3. y(32) = 22.0948
4. Sn = [n(n+1)/2]2
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