Newton interpolation polynomial

The Newton interpolation polynomial is a way to find a polynomial that passes through a given set of points. It builds the polynomial step by step using special numbers called divided differences, which help to easily add more points if needed.

Important properties

• The Newton form of the interpolation polynomial is especially useful when new data points are added, as it allows easy updating.

• The polynomial is written as a sum of terms, each involving products of $(x - x_i)$ for previous points.

• Divided differences are used to calculate the coefficients efficiently.