Which interpolation formula does not have any difference operator?

Concept:

Given (x0 ,y0 ), (x1 ,y1 ), …, (xn ,yn), finding the value of ‘y’ at a value of ‘x’ in (x0, xn ) is called interpolation.

Calculations:

Given (x₀ ,y₀ ), (x₁ ,y₁ ), …, (x_n ,y_n), finding the value of ‘y’ at a value of ‘x’ in (x₀, x_n ) is called interpolation.

Newton - forward Interpolation formula have difference operator

This is particularly useful for interpolating the values of f(x) near the beginning of the set of values given. h is called the interval of difference and u = ( x – a ) / h, Here a is the first term.

Bessel's Interpolation formula have difference operator.

This formula involves means of even difference on and below the central line and odd difference below the line.

Stirling Formula have difference operator.

Stirling Formula is obtained by taking the average or mean of the Gauss Forward and Gauss Backward Formula.

Lagrange's Interpolation formula has no difference operator.

Lagrange's Interpolation formula used to interpolate between data pairs (x0 ,f(x0 )), (x1 ,f(x1 )),…, (xn ,f(xn )) is given by, Where the polynomial Pj (x) is given by,

 p(x) = \(\rm\sum\)p_j (x) , j = 1, 2, ....