I have explained the newton interpolation program in c programming here in this post. This tutorial helps computer science students understand the concepts of interpolation, extrapolation in numerical techniques.

This tutorial helps the students implement the program for backward interpolation in the c programming language.

Newton Backward Interpolation Program in C

What is Interpolation ?

Given the set of (n+1) values of x and y, it is required to find y n (x), a polynomial of the nth Degree such that y and y n (x) agree at the tabulated points. The values of x be equidistant i.e. xi = x0 + ih, i=0, 1, 2…..n.

Since y n(x) is a polynomial of the nth Degree

y n(x) =a0 +a1(x-x0) +a2(x-x0)(x-x1)………….+an(x-x0)………….(x-x n-1)

Imposing now the condition that y and yn(x) should agree at the set of tabulated points and applying x=x0+ph, we get Newton’s Forward difference interpolation formula which is given by.

y n(x) = y0 + pDy0 + p (p-1) / 2! D2y0+ p (p-1) (p-2) / 3! D3y0 + ……… + p (p-1) (p-2)…. (p-n+1) / n! Dn y0

It is helpful for interpolation near the beginning of a set of tabular values.

Similarly, if you (x) chosen in the form

y n(x) = a0+a1 (x-x n) + a2 (x-x n) (x-x n-1) +……..an(x-x n) (x-x n-1)……(x-x1) 

then we have

y n (x) = y n + pÑy n + p(p+1) / 2 Ñ2 y n + ………+ p(p+1)…..(p+n-1) / n! Ñ n y n   

where p= x-x n / h

This is newton’s backward difference interpolation formula, and it uses tabular values to the left of y n. It is helpful for interpolation near the end of the tabular values.

Void Main()

                    for(i=0; i <n; i++)   {
                                  printf(“/n nenter the value of x%d: “,i);