Remez algorithm: Difference between revisions

Revision as of 12:37, 19 March 2022

Revision as of 19:47, 22 April 2022

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==Variants==

Some modifications of the algorithm isare present on the literature.<ref>{{Citation |last=Egidi |first=Nadaniela |title=A New Remez-Type Algorithm for Best Polynomial Approximation |date=2020 |url=http://link.springer.com/10.1007/978-3-030-39081-5_7 |work=Numerical Computations: Theory and Algorithms |volume=11973 |pages=56–69 |editor-last=Sergeyev |editor-first=Yaroslav D. |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-030-39081-5_7 |isbn=978-3-030-39080-8 |access-date=2022-03-19 |last2=Fatone |first2=Lorella |last3=Misici |first3=Luciano |editor2-last=Kvasov |editor2-first=Dmitri E.}}</ref> These include:

* Replacing more than one sample point with the locations of nearby maximum absolute differences.{{Citation needed|date=March 2022}}

* Replacing all of the sample points with in a single iteration with the locations of all, alternating sign, maximum differences.<ref name="toobs">2/73Temes, G.C.; Barcilon, V.; Marshall, F.C. (1973). "The Optimizationoptimization of Bandlimitedbandlimited Systemssystems" – G. C.''Proceedings Temes,of F.the CIEEE''. Marshall'''61''' and(2): V196–234. Barcilon[[Doi (identifier)|doi]]:10.1109/PROC.1973.9004. [[ISSN Proceedings IEEE(identifier)|ISSN]]&nbsp;0018-9219.</ref>

* Using the relative error 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;

* Including zero-error point constraints.<ref name="toobs" />

* The Fraser-Hart variant, used to determine the best rational Chebyshev approximation.<ref>{{Cite journal |last=Dunham |first=Charles B. |date=1975 |title=Convergence of the Fraser-Hart algorithm for rational Chebyshev approximation |url=https://www.ams.org/mcom/1975-29-132/S0025-5718-1975-0388732-9/ |journal=Mathematics of Computation |language=en |volume=29 |issue=132 |pages=1078–1082 |doi=10.1090/S0025-5718-1975-0388732-9 |issn=0025-5718}}</ref>

==See also==