←

Maths for Engineers - 3

# Problems On Interpolation Method

**Problems on Interpolation Method-1:**

**Example-3** Show that, the nth divided difference of a polynomial of the nth degree is constant

Solution: Let the arguments be equally spaced so that x_{1} − x_{0} = x_{2} − x_{1} = ... = h. Then

and in general,

If the tabulated function is a nth degree polynomial, then△^{n}y_{0} will be constant. Here the nth divided differences will also be constant.

**Example-4** Using the following table find f (x) as a polynomial in x.

**Solution: **The divided difference table is

Therefore by Newton’s Divided Difference Formula,