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{{Short description|Algorithm to approximate functions}}
The '''Remez algorithm''' or '''Remez exchange algorithm''', published by [[Evgeny Yakovlevich Remez]] in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a [[Chebyshev space]] that are the best in the [[uniform norm]] ''L''<sub>∞</sub> sense.<ref>{{cite journal |author-link=Evgeny Yakovlevich Remez |first=E. Ya. |last=Remez |title=Sur la détermination des polynômes d'approximation de degré donnée |journal=Comm. Soc. Math. Kharkov |volume=10 |pages=41 |date=1934 }}<br/>{{cite journal |author-mask=1 |first=E. |last=Remes (Remez) |title=Sur un procédé convergent d'approximations successives pour déterminer les polynômes d'approximation |journal=Compt. Rend. Acad. Sci. |volume=198 |pages=2063–5 |language=fr |date=1934 |url=https://gallica.bnf.fr/ark:/12148/bpt6k31506/f2063.item}}<br/>{{cite journal |author-mask=1 |first=E. |last=Remes (Remez) |title=Sur le calcul effectif des polynomes d'approximation de Tschebyschef |journal=Compt. Rend. Acad. Sci. |volume=199 |issue= |pages=337–340 |language=fr |date=1934 |url=https://gallica.bnf.fr/ark:/12148/bpt6k3151h/f337.item}}</ref> It is sometimes referred to as '''Remes algorithm''' or '''Reme algorithm'''.<ref>{{
A typical example of a Chebyshev space is the subspace of [[Chebyshev polynomials]] of order ''n'' in the [[Vector space|space]] of real [[continuous function]]s on an [[interval (mathematics)|interval]], ''C''[''a'', ''b'']. The polynomial of best approximation within a given subspace is defined to be the one that minimizes the maximum [[absolute difference]] between the polynomial and the function. In this case, the form of the solution is precised by the [[equioscillation theorem]].
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