Newton polynomial

In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated using Newton's divided differences method. Definition Given a set of k + 1 data points where no two xj are the same, the Newton interpolation polynomial is a linear combination of Newton basis polynomials with the Newton basis polynomials defined as