Chapter 21 Polynomial Interpolation
The main goal of this part of the course is to find some reasonable function that matches the given data points, perhaps approximately. Such a function may be used for making predictions about the future, or to fill the gaps between the data points (for example, estimate the population in a year when there was no census). It can also be used for numerical calculus: integration or differentiation.
Polynomials are the simplest nonlinear functions, so when we look for a simple function that could fit our data, it is natural to reach for polynomials. It turns out polynomials are not as simple as they appear at first.