Minimax approximation algorithm: Difference between revisions

Revision as of 15:30, 30 August 2012

Revision as of 13:33, 3 September 2012

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{{Context|date=October 2009}}

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 }}</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 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>