Approximation theory is a field of mathematics which is concerned with approximating the values of a function. Usually, the approximation is only needed for a range of values or domain. A good approximation will only have a small error in the domain of interest.
There are different ways in which this approximation is done: common ones are using a combination of simpler functions or using polynomials.
- Trefethen, L. N. (2019). Approximation theory and approximation practice. Society for Industrial and Applied Mathematics.