Newton polynomial - Wikipedia
https://en.wikipedia.org/wiki/Newton_polynomialAs with other difference formulas, the degree of a Newton interpolating polynomial can be increased by adding more terms and points without discarding existing ones. Newton's form has the simplicity that the new points are always added at one end: Newton's forward formula can add new points to the right, and Newton's backward formula can add new points to the left. The accuracy of polynomial interpolation depends on how close the interpolated point is to the …
Newton's Interpolation Formulae
www.nptel.ac.in › content › storage2EXERCISE 11. 4. 2 Derive the Newton's backward interpolation formula for Remark 11 . 4 . 3 If the interpolating point lies closer to the beginning of the interval then one uses the Newton's forward formula and if it lies towards the end of the interval then Newton's backward formula is used.