The standard approach to minimax approximations is called the "Remez Exchange Algorithm" (or Remez algorithm, or Remes algorithm). It can be fussy, however, an

The standard approach to minimax approximations is called the "Remez Exchange Algorithm" (or Remez algorithm, or Remes algorithm). It can be fussy, however, and often requires a knowledgeable user to product good results, which is why Chebyshev and Cathedory-Fejer approximants are often used instead -- they are very nearly as good, and much easier to compute.