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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>E. Ya. Remez, "Sur la détermination des polynômes d'approximation de degré donnée", Comm. Soc. Math. Kharkov '''10''', 41 (1934);<br/>"Sur un procédé convergent d'approximations successives pour déterminer les polynômes d'approximation, Compt. Rend. Acad. Sc. '''198''', 2063 (1934);<br/>"Sur le calcul effectiv des polynômes d'approximation des Tschebyscheff", Compt. Rend. Acade. Sc. '''199''', 337 (1934).</ref> It is sometimes refered to as '''Remes algorithm''' or '''Reme algorithm'''.
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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