Newton's Divided Differences is a method for constructing polynomial interpolants of a given set of data points, allowing for efficient computation of coefficients in Newton's interpolating polynomial form. This approach is particularly useful for its recursive nature and its ability to handle unequally spaced data points, making it a versatile tool in numerical analysis.
Extrapolation is a statistical method used to predict or estimate values outside the range of known data points by extending a trend or pattern. It relies on the assumption that the established trend continues beyond the observed data, which can lead to inaccuracies if the underlying assumptions do not hold true.