Minimax approximation algorithm

A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a <a href="/facts/Mathematical_function/CdReEKCh">mathematical function</a> that minimizes maximum error.
For example, given a function 
 
 
 
 f
 
 
 {\displaystyle f}
 
 defined on the interval 
 
 
 
 [
 a
 ,
 b
 ]
 
 
 {\displaystyle [a,b]}
 
 and a degree bound 
 
 
 
 n
 
 
 {\displaystyle n}
 
, a minimax polynomial approximation algorithm will find a polynomial 
 
 
 
 p
 
 
 {\displaystyle p}
 
 of degree at most 
 
 
 
 n
 
 
 {\displaystyle n}
 
 to minimize

max
 
 a
 ≤
 x
 ≤
 b
 
 
 
 |
 
 f
 (
 x
 )
 −
 p
 (
 x
 )
 
 |
 
 .
 
 
 {\displaystyle \max _{a\leq x\leq b}|f(x)-p(x)|.}
 
<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a>

Minimax approximation algorithm open-in-new

Minimax approximation algorithm