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∞ sense.[1] It is sometimes referred to as Remes algorithm or Reme algorithm.[citation needed]
A typical example of a Chebyshev space is the subspace of Chebyshev polynomials of order n in the space of real continuous functions on an 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.
^E. Ya. Remez, "Sur la détermination des polynômes d'approximation de degré donnée", Comm. Soc. Math. Kharkov 10, 41 (1934); "Sur un procédé convergent d'approximations successives pour déterminer les polynômes d'approximation, Compt. Rend. Acad. Sc. 198, 2063 (1934); "Sur le calcul effectiv des polynômes d'approximation des Tschebyscheff", Compt. Rend. Acade. Sc. 199, 337 (1934).
The Remezalgorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations...
Clenshaw–Curtis quadrature, a numerical integration technique. The Remezalgorithm (sometimes spelled Remes) is used to produce an optimal polynomial...
scientist, theoretician and teacher RemezalgorithmRemez inequality This page lists people with the surname Remez. If an internal link intending to refer...
fit of degree larger than 1, computing the coefficients using the Remezalgorithm. The trade-off is that the initial guess requires more computational...
the minimax polynomial. One popular minimax approximation algorithm is the Remezalgorithm. Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent;...
in the constructive function theory, in particular, for the Remezalgorithm and the Remez inequality. His doctoral students include Boris Korenblum. Cheney...
design than IIR filters - the Parks-McClellan filter design algorithm (based on the Remezalgorithm) is one suitable method for designing quite good filters...
-1 or +1. Several minimax approximation algorithms are available, the most common being the Remezalgorithm. Golomb, Michael (1962). Lectures on Theory...
Bernstein's constant — error when approximating |x| by a polynomial Remezalgorithm — for constructing the best polynomial approximation in the L∞-norm...
usually a Taylor polynomial or a Chebyshev polynomial derived by the Remezalgorithm (having the benefit of an improved error bound), but the pre-processing...
rounded libm), and its successor MetaLibm and finally CORE-MATH. Uses Remezalgorithm to automatically generate approximations that are formally proven....
(also known as the equiripple, optimal, or minimax method). The Remez exchange algorithm is commonly used to find an optimal equiripple set of coefficients...
The pattern playback was last used in an experimental study by Robert Remez in 1976. The pattern playback now resides in the Museum at Haskins Laboratories...
physics: 35 Robert Remak (1888–1942), algebra and mathematical economics Evgeny Remez (1895–1975), constructive function theory Alfréd Rényi (1921–1970), combinatorics...
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