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Learn Newton's divided difference polynomial method by following the linear interpolation example. For more videos and resources on this topic, please visit. An example for a a quadratic polynomial , , interpolation would be the following The coefficients needed to construct Newton's polynomial is the top diagonal of the divided-difference matrix. The same thing happens with Lagrange Interpolation that happened in Vandermonde Matrix. Interpolation functions are defined for each element to interpolate, for values inside the. C Program for Newton Forward Interpolation. Interpolation is the process of finding the values of y corresponding to the any value of x between x0 and xn for the given values of y=f (x) for a set of values of x. Out of the many. P n ( x 1) = ∑ k = 0 n α k e k ( x 1) = α 0 + α 1 ( x 1 − x 0) = f [ x 0] + α 1 ( x 1 − x 0) = f [ x 1] Hence. α 1 = f [ x 1] − f [ x 0] x 1 − x 0 = f [ x 0, x 1] f [ x 0, x 1] is called 1 s t - order divided difference. Newton’s interpolation polynomial of degree n, P n ( x), evaluated at x 2, gives:. Newton’s divided difference interpolation formula is a interpolation technique used when the interval difference is not same for all sequence of values. Suppose f(x 0 ), f(x 1 ), f(x 2 )f(x n ) be the (n+1) values of the function y=f(x) corresponding to the arguments x=x 0 , x 1 , x 2 x n , where interval differences are not same. Newton's Interpolation Formulae As stated earlier, interpolation is the process of approximating a given function, whose values are known at tabular points, by a suitable polynomial, of degree which takes the values at for Note that if the given data has errors, it will also be reflected in the polynomial so obtained.. In the following, we shall use forward and backward differences to.