Minimax approximation algorithm: Difference between revisions

Revision as of 18:20, 29 August 2012

Revision as of 18:27, 29 August 2012

Line 1:

{{unreferenced|date=August 2012}}

{{Context|date=October 2009}}

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<ref>{{cite book | chapter = 7: The theory of minimax approximation | first = M. J. D. | last= Powerll | year = 1981 | publisher= Cambridge University Press | title = Approximation Theory and Methods | isbn = 0521295149}}</ref>

::<math>\max_{a \leq x \leq b}|f(x)-p(x)|.</math>

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.

Algorithms that minimize the maximum error are known as '''Minimax approximation algorithms'''. One popular approach is the [[Remez algorithm]].

==External links==

*[http://mathworld.wolfram.com/MinimaxApproximation.html Minimax approximation algorithm at MathWorld]

==References==

{{Reflist}}

[[Category:Numerical analysis]]