|
|
| Line 1: |
Line 1: |
| A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref>{{cite book | title = Handbook of Floating-Point Arithmetic | page = 376 | publisher = Springer | year = 2009 | isbn = 081764704X | first1=Jean-Michel | last1=Muller|last2=Brisebarre | first2=Nicolas | last3=de Dinechin | first3=Florent | last4=Jeannerod | first4=Claude-Pierre | last5=Lefèvre | first5=Vincent | last6=Melquiond | first6=Guillaume | last7=Revol | first7=Nathalie | last8=Stehlé | first8=Damien | last9=Torres | first9=Serge | display-authors=1 }}</ref> or '''uniform approximation'''<ref name="phillips">{{cite doi | 10.1007/0-387-21682-0_2}}</ref>) 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 find a function p(''x'') to minimize<ref name="powell">{{cite book | chapter = 7: The theory of minimax approximation | first = M. J. D. | last= Powell | authorlink=Michael J. D. Powell | year = 1981 | publisher= Cambridge University Press | title = Approximation Theory and Methods | isbn = 0521295149}}</ref>
| | Marvella is what you can call her but it's not the most female name out there. What I adore performing is taking part in baseball but I haven't made a dime with it. South Dakota is exactly where me and my husband reside and my family loves it. For many years I've been working as a payroll clerk.<br><br>Also visit my web blog - [http://www.videoworld.com/blog/211112 at home std testing] |
| ::<math>\max_{a \leq x \leq b}|f(x)-p(x)|.</math>
| |
| | |
| ==Polynomial approximations==
| |
| | |
| 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" />
| |
| | |
| 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 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==
| |
| *[http://mathworld.wolfram.com/MinimaxApproximation.html Minimax approximation algorithm at MathWorld]
| |
| | |
| ==References==
| |
| | |
| {{Reflist}}
| |
| | |
| [[Category:Numerical analysis]]
| |
| | |
| | |
| {{algorithm-stub}}
| |
Latest revision as of 14:05, 5 May 2014
Marvella is what you can call her but it's not the most female name out there. What I adore performing is taking part in baseball but I haven't made a dime with it. South Dakota is exactly where me and my husband reside and my family loves it. For many years I've been working as a payroll clerk.
Also visit my web blog - at home std testing