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Remez algorithm
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<p>The Remez algorithm or Remez exchange algorithm, published by <a href="/facts/Evgeny_Yakovlevich_Remez/xn2VGvjB">Evgeny Yakovlevich Remez</a> in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a <a href="/facts/Chebyshev_space/vdKuTjBS">Chebyshev space</a> that are the best in the <a href="/facts/Uniform_norm/5yIkjNE3">uniform norm</a> <i>L</i>∞ sense. It is sometimes referred to as Remes algorithm or Reme algorithm. </p><p>A typical example of a Chebyshev space is the subspace of <a href="/facts/Chebyshev_polynomials/HoBINqgC">Chebyshev polynomials</a> of order <i>n</i> in the <a href="/facts/Vector_space/M1pxMLx2">space</a> of real <a href="/facts/Continuous_function/sKbl02pB">continuous functions</a> on an <a href="/facts/Interval_(mathematics)/e9se3vTe">interval</a>, <i>C</i>[<i>a</i>, <i>b</i>]. The polynomial of best approximation within a given subspace is defined to be the one that minimizes the maximum <a href="/facts/Absolute_difference/2AdTdj8a">absolute difference</a> between the polynomial and the function. In this case, the form of the solution is precised by the <a href="/facts/Equioscillation_theorem/LYMS65P7">equioscillation theorem</a>. </p>