Remez Algorithm

The Remez algorithm, or Remez exchange algorithm, published by Evgeny Remez in 1934, is an iterative algorithm used to find the simplest approximations to functions, specifically the best approximation in the uniform norm sense by functions drawn from a Chebyshev space. A typical example of such a space is the set of Chebyshev polynomials of a given order within the space of real continuous functions on an interval, and the polynomial of best approximation is defined as the one minimizing the maximum absolute difference between the polynomial and the function, a form of solution characterized by the equioscillation theorem.