Newton polynomial
isaac newton
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Newton polynomial
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is the interpolation polynomial for a given set of data points in the Newton form. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated using divided differences. (The other difference formulas, such as those of Gauss, Bessel and Stirling, can be derived from Newton's, by renaming of the x-values of the data points.) For any given finite set of data points, there is only one polynomial, of least possible degree, that passes through all of them. Thus, it is more appropriate to speak of "the Newton form of the interpolation polynomial" rather than of "the Newton interpolation polynomial". Like the Lagrange form, it is merely another way to write the same polynomial.