Newton's divided differences

Newton's divided differences are a method used in numerical analysis to construct polynomial functions that pass through a set of data points. They help in approximating complex functions with simpler polynomials by calculating successive differences between data values. These differences build a structured table, which then allows us to efficiently evaluate the polynomial at any point or interpolate missing data. Essentially, divided differences provide a systematic way to understand the incremental changes in data, enabling smooth interpolation and approximation of functions based on discrete data points.