DeepAI AI Chat
Log In Sign Up

An algorithm for real and complex rational minimax approximation

by   Yuji Nakatsukasa, et al.
University of Oxford

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.


page 1

page 2

page 3

page 4


Flexible rational approximation for matrix functions

A rational approximation is a powerful method for estimating functions u...

An algorithm for best generalised rational approximation of continuous functions

The motivation of this paper is the development of an optimisation metho...

AAA-least squares rational approximation and solution of Laplace problems

A two-step method for solving planar Laplace problems via rational appro...

Rational approximation of the absolute value function from measurements: a numerical study of recent methods

In this work, we propose an extensive numerical study on approximating t...

Exponential node clustering at singularities for rational approximation, quadrature, and PDEs

Rational approximations of functions with singularities can converge at ...

Approximating the pth Root by Composite Rational Functions

A landmark result from rational approximation theory states that x^1/p o...

A comparison of rational and neural network based approximations

Rational and neural network based approximations are efficient tools in ...