IGNOU BMTE 144 2026 - Find the interpolating polynomial by Newton’s divided difference

Question

Find the interpolating polynomial by Newton’s divided difference formula for the following data:

x	0	1	2	4
y	1	1	2	5

09 Jan 2026

Answer :

Word Count : 277

We are given the data: [ \begin{array}{c|cccc} x & 0 & 1 & 2 & 4 \ \hline y & 1 & 1 & 2 & 5 \end{array} ] We will use Newton’s divided difference formula. Step 1: Construct the divided difference table. [ \begin{array}{c|c|c|c|c} x & f[x_i] & f[x_i,x_{i+1}] & f[x_i,x_{i+1},x_{i+2}] & f[x_i,x_{i+1},x_{i+2},x_{i+3}] \ \hline 0 & 1 & & & \ 1 & 1 & & & \ 2 & 2 & & & \ 4 & 5 & & & \ \end{array} ] Step 2: First divided differences (f[x_i,x_{i+1}] = \frac{f[x_{i+1}] - f[x_i]}{x_{i+1}-x_i}) [ f[0,1] = \frac{1-1}{1-0} = 0 ] [ f[1,2] = \frac{2-1}{2-1} =

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