An algorithm for real and complex rational minimax approximation

Journal article

Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the AAA-Lawson algorithm available in Chebfun. The new algorithm solves a wide range of problems on arbitrary domains in a fraction of a second of laptop time by a procedure consisting of two steps. First, the standard AAA algorithm is run to obtain a near-best approximation and a set of support points for a barycentric representation of the rational approximant. Then a "Lawson phase" of iteratively reweighted least-squares adjustment of the barycentric coefficients is carried out to improve the approximation to minimax.

Authors: Nakatsukasa, Y; Trefethen, LN

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Journal on Scientific Computing
• Volume: 42
• Issue: 5
• Pages: A3157-A3179
• Publication date: 2020-10-13
• Acceptance date: 2020-07-08
• DOI: 10.1137/19M1281897
• EISSN: 1095-7197
• ISSN: 1064-8275
• Language: English
• Keywords: rational approximation; barycentric formula; FFR; AAA algorithm; AAA-Lawson algorithm; iteratively reweighted least-squares
• Subjects: 65D15; 41A20