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Using data points in which the independent variable x are equally spaced simplifies finding the quadratic interpolation polynomial using Newton's Divided Difference technique. Two levels of divided differences are required for the quadratic solution.
Example : Compute f (0.3) for the data. using Newton's divided difference formula. Solution : Divided difference table. Now Newton's divided difference formula is. f (x) = f [x0] + (x - x0) f [x0, x1] + (x - x0) (x - x1) f [x0, x1, x2] + (x - x0) (x - x1) (x - x2)f [x0, x1, x2, x3]
Using Newton's divided difference formula, find u (3) given u (1) = -26, ad u (2) = 12, u (4) = 256, u (6) = 844. [A.U. April/May 2004] Solution: We form the divided difference table, since the intervals are unequal. 2. Find f (x) as a polynomial in x for the following data by Newton's divided difference formula. 3.
23 Νοε 2009 · Determine the value of the specific heat at T 61 C using Newton’s divided difference method of interpolation and a second order polynomial. Find the absolute relative
9 Οκτ 2021 · In this post, we have two solved problems as an application to Newton-divided differences. The first solved problem. Three points where x and y values are given are required to get the expression for the polynomial based on Newton-divided differences and the value of a new point with x=2.70.
14 Νοε 2022 · NEWTON’S DIVIDED DIFFERENCE INTERPOLATION FORMULA. Examples: Input: Value at 7 Output: Value at 7 is 13.47. Below is the implementation of Newton’s divided difference interpolation method.
Using the divided difference notation we see that a 0 = f[x 0] a 1 = f[x 0,x 1] a 2 = f[x 0,x 1,x 2]... a n = f[x 0,x 1,x 2,...,x n], and thus P n(x) = f[x 0] + Xn k=1 f[x 0,...,x k] kY−1 j=0 (x −x j). This is called Newton’s interpolatory divided difference formula.
