Minimax approximation algorithm: Difference between revisions

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A '''minimax approximation algorithm''' (or '''L^∞ 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">{{citeCite doibook | doi = 10.1007/0-387-21682-0_2 | first = George M. | last = Phillips| chapter = Best Approximation | title = Interpolation and Approximation by Polynomials | series = CMS Books in Mathematics | pages = 49–11 | year = 2003 | publisher = Springer | isbn = 0-387-00215-4 | pmid = | pmc = }}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.

For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> 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>