Minimax approximation algorithm

A minimax approximation algorithm is a method which aims to find an approximation such that the maximum error is minimized. Suppose we seek to approximate the function f(x) by a function p(x) on the interval [a,b]. Then a minimax approximation algorithm will aim to minimize

$\max _{a\leq x\leq b}|f(x)-p(x)|.$

Polynomial expansions such as the Taylor series expansion are often convenient for theoretical work but less useful for practical applications. For practical work it is often desirable to minimize the maximum absolute or relative error of a polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation.

One popular approach is the Remez algorithm.

External links

• Minimax approximation algorithm at MathWorld