Newton polynomial

Summary

The Newton polynomial is the interpolation polynomial of given data written in the Newton form. The basis is $1$, $(x - x_0)$, $(x - x_0)(x - x_1)$, and so on, and the coefficients are divided differences. Adding one more data point adds one more term and leaves the earlier terms unchanged. This makes the Newton form convenient for computation and for deriving error terms and finite difference formulas.