Minimax approximation algorithm: Difference between revisions

Revision as of 20:14, 29 November 2014

Revision as of 09:46, 7 December 2014

Line 7:

The [[Weierstrass approximation theorem]] states that every continuous function defined on a closed interval [a,b] can be uniformly approximated as closely as desired by a polynomial function.<ref name="phillips" />

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.

Polynomial expansions such as the [[Taylor series]] expansion are often convenient for theoretical work but less useful for practical applications. ForTruncated practical[[Chebyshev workseries]], ithowever, isclosely often desirable to minimizeapproximate the maximum absolute or relative error of aminimax polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation.

One popular minimax approximation algorithm is the [[Remez algorithm]]. [[Chebyshev polynomials of the first kind]] closely approximate the minimax polynomial.<ref>{{cite web | url = http://mathworld.wolfram.com/MinimaxPolynomial.html | title = Minimax Polynomial | publisher = Wolfram MathWorld | accessdate= 2012-09-03}}</ref>

==External links==