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AN ALGORITHM FOR REAL AND COMPLEX RATIONAL MINIMAX APPROXIMATION
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DOI：10.1137/19M1281897.png)
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Abstract
En 中文
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 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.
Keywords:
rational approximation
barycentric formula
AAA algorithm
AAA-Lawson algorithm
iteratively reweighted least-squares
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