Title :

Rational Minimax Approximation via Adaptive Barycentric Representations

Author(s) :

Filip, Silviu-Ioan [Auteur]
Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources [CAIRN]
Nakatsukasa, Yuji [Auteur]
Mathematical Institute [Oxford] [MI]
Trefethen, Lloyd Nicholas [Auteur]
Mathematical Institute [Oxford] [MI]
Beckermann, Bernhard [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

SIAM Journal on Scientific Computing

Pages :

A2427-A2455

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2018-08-07

ISSN :

1064-8275

English keyword(s) :

barycentric formula
rational minimax approximation
Remez algorithm
differential correction algorithm
AAA algorithm
Lawson algorithm

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. ...
Show more >Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far more robust algorithms than previously available can be developed by making use of rational barycentric representations whose support points are chosen in an adaptive fashion as the approximant is computed. Three variants of this barycentric strategy are all shown to be powerful: (1) a classical Remez algorithm, (2) a "AAA-Lawson" method of iteratively reweighted least-squares, and (3) a differential correction algorithm. Our preferred combination, implemented in the Chebfun MINIMAX code, is to use (2) in an initial phase and then switch to (1) for generically quadratic convergence. By such methods we can calculate approximations up to type (80, 80) of |x| on [−1,1] in standard 16-digit floating point arithmetic, a problem for which Varga, Ruttan, and Carpenter required 200-digit extended precision.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Comment :

Author files.

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL