Remez algorithm: Difference between revisions

Revision as of 16:30, 27 November 2006

Revision as of 19:01, 16 December 2006

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The '''Remez algorithm''', published by [[Evgeny Yakovlevich Remez]] in [[1934]]<ref>E. Ya. Remez, "Sur la d&eacute;termination des polyn&ocirc;mes d'approximation de degr&eacute; donn&eacute;e", Comm. Soc. Math. Kharkov '''10''', 41 (1934);<br>"Sur un proc&eacute;d&eacute; convergent d'approximations successives pour d&eacute;terminer les polyn&ocirc;mes d'approximation, Compt. Rend. Acad. Sc. '''198''', 2063 (1934);<br>"Sur le calcul effectiv des polyn&ocirc;mes d'approximation des Tschebyscheff, Compt. Rend. Acade. Sc. '''199''', 337 (1934).</ref> (also called the '''Remez exchange algorithm''') is an iterative algorithm for best approximation in the [[uniform norm]] ''L''_&infin; in the [[Chebyshev space]]. A typical example of Chebyshev space is the subspace of polynomial of order ''n'' in the space of real continuous function on an interval, ''C''[a, b].

The '''Remez algorithm''' (Remez 1934), also called the '''Remez exchange algorithm''', is an iterative algorithm that finds the polynomial of best approximation of a given degree to a real function on an interval.

The algorithm is named after its author—E.Ya.Remez, Soviet mathematician.

The polynomial of best approximation of a given degree is defined to be the one that minimizes the maximum absolute difference between the polynomial and the function.

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Sometimes [[relative error]] is used to measure the difference between the approximation and the function, especially if the approximation will be used to compute the function on a computer which uses [[floating-point]] arithmetic.

==References==

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==External links==