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Reference: Ricardo Pachόn and Nick Trefethen, (2008). Barycentric−Remez algorithms for best polynomial approximation in the chebfun system.Citable link to this page:

 

Barycentric−Remez algorithms for best polynomial approximation in the chebfun system

Abstract: Variants of the Remez algorithm for best polynomial approximation are presented based on two key features: the use of the barycentric interpolation formula to represent the trial polynomials, and the setting of the whole computation in the chebfun system, where the determination of local and global extrema at each iterative step becomes trivial. The new algorithms make it a routine matter to compute approximations of degrees in the hundreds, and as an example, we report approximation of |x| up to degree 10,000. Since barycentric formulas can also represent rational functions, the algorithms we introduce may also point the way to new methods for computing best rational approximations.

Bibliographic Details

Publisher: Oxford University Computing Laboratory

Issue Date: 2008-12-01Identifiers

Urn: uuid:d9155ed3-481f-473b-b45f-1cdb35a8c6d8 Item Description

Type: Report; Tiny URL: cs:2859

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Author: Ricardo Pachόn - - - Nick Trefethen - - - - Bibliographic Details Publisher: Oxford University Computing Laboratory - - Issue Da

Source: https://ora.ox.ac.uk/objects/uuid:d9155ed3-481f-473b-b45f-1cdb35a8c6d8



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