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Author Smith, L. B. ♦ Golub, G. H.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Approximation ♦ Chebyshev approximation ♦ Remez algorithm
Abstract The second algorithm of Remez can be used to compute the minimax approximation to a function, ƒ(x), by a linear combination of functions, {Qi(x)}n0, which form a Chebyshev system. The only restriction on the function to be approximated is that it be continuous on a finite interval [a,b]. An Algol 60 procedure is given, which will accomplish the approximation. This implementation of the second algorithm of Remez is quite general in that the continuity of ƒ(x) is all that is required whereas previous implementations have required differentiability, that the end points of the interval be “critical points,” and that the number of “critical points” be exactly n + 2. Discussion of the method used and of its numerical properties is given as well as some computational examples of the use of the algorithm. The use of orthogonal polynomials (which change at each iteration) as the Chebyshev system is also discussed.
Description Affiliation: Stanford Univ., CA (Golub, G. H.) || Univ. of Colorado, Boulder (Smith, L. B.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 14
Issue Number 11
Page Count 10
Starting Page 737
Ending Page 746


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Source: ACM Digital Library