Minimax approximation

Summary

Fix a continuous function $f$ on an interval and a degree $n$. A minimax approximation of $f$ is a polynomial $p$ of degree at most $n$ that makes the largest error $\max \abs{f - p}$ as small as possible. It is the best approximation for the uniform norm, so it controls the error at every point and not only on average. Minimax polynomials are used to build the routines that compute $\sin$, $\exp$ and other functions in software libraries.