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Gareth Jones (talk | contribs) clarify algorithm finds p(x) |
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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>
::<math>\max_{a \leq x \leq b}|f(x)-p(x)|.</math>
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