Newton's backward interpolation method uses equidistant points to calculate backward differences, where the first backward difference is the difference between consecutive y-values and the second backward difference is the difference between first backward differences. The Newton backward interpolation formula can be used to find the value of y at a given x, such as using a table of backward differences to calculate the value of y when x is 35 based on the provided data points of x, y pairs.

1. Newton's Backward
Interpolation
Method
Muhammad Umair F2016266123

2. Interpolation

3. Let us take the equi-spaced points x0 ,
x1 = x0 + h, x2 = x1 + h, ......................, xn =
xn - 1 + h
Then ⛛ yn = ⛛ yn -⛛ yn - 1 is called the first backward
difference
i.e. ⛛ y1 = y1 - y0 , y2 = y2 - y1 and so on.
⛛ 2 yn = ⛛ yn - ⛛ yn - 1 is called the second backward
difference
i.e. ⛛ 2 y1 = ⛛ y1 - ⛛ y0 , ⛛2 y2 = ⛛ y2 - ⛛ y1 and so on
X Y
0 7
10 18
20 32
30 48
40 85

4. Newton Backward Interpolation formula:

5. Example:
Using following data to find the value of y at x = 35
Solution:

6. Backward Difference Table:

8. Thankyou!