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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 x1 − x0 = x2 − x1 = ... = h. Then
and in general,
If the tabulated function is a nth degree polynomial, then△ny0 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,
