Applications of AAA rational approximation

2025/10/17 by Nakatsukasa, Yuji, Trefethen, Lloyd N. · 4 citations
#41A20 #65D15 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2510.16237

Abstract

The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.

Citations

• RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains
• Steady advection-diffusion in multiply-connected potential flows
• Small-time asymptotics and the emergence of complex singularities for the KdV equation
• Numerical conformal mapping
• Quadrature formulas from rational approximations
• Efficient time-domain scattering synthesis via frequency-domain singularity subtraction
• Unbounded growth of band-limited functions
• Numerical computation of the Schwarz function
• Resonance modes in microstructured photonic waveguides: Efficient and accurate computation based on AAA rational approximation
• Resonance modes in microstructured photonic waveguides: efficient and accurate computation based on AAA rational approximation
• Acoustic wave diffraction by a quadrant of sound-soft scatterers
• Polynomial approximation of noisy functions
• Modelling wildfire spread and spotfire merger using conformal mapping and AAA-least squares methods
• Computing Stokes flows in periodic channels via rational approximation
• Efficient Rational Approximation of Optical Response Functions with the AAA Algorithm
• A modified AAA algorithm for learning stable reduced-order models from data
• Multivariate rational approximation of functions with curves of singularities
• Diffraction of acoustic waves by multiple semi-infinite arrays
• AAA interpolation of equispaced data
• Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation
• Numerical Continued Fraction Interpolation
• The Wiener--Hopf Technique, its Generalisations and Applications: Constructive and Approximate Methods
• Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework
• The AAAtrig algorithm for rational approximation of periodic functions
• Exponential node clustering at singularities for rational approximation,\n quadrature, and PDEs
• Rational neural networks
• Numerical conformal mapping with rational functions
• Quantifying the ill-conditioning of analytic continuation
• SciPy 1.0: fundamental algorithms for scientific computing in Python
• Representation of conformal maps by rational functions
• Automatic rational approximation and linearization of nonlinear\n eigenvalue problems
• Computational Methods for Linear Matrix Equations
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
• Analysis of series expansions for non-algebraic singularities
• NLEVP
• On the use of rational-function fitting methods for the solution of 2D\n Laplace boundary-value problems

Cited by

• L² and L^∞ rational approximation
• Rational Minimax Approximations for Matrix-Valued Functions: Existence, Optimality and Algorithms
• The Loewner framework applied to Zolotarev sign and ratio problems
• Multivariate Rational Approximation of Scattered Data Using the p-AAA Algorithm
• Greedy Thiele continued-fraction approximation on continuum domains in the complex plane

Related

• Rational approximation
• The first five years of the AAA algorithm
• Two intriguing variants of the AAA algorithm for rational approximation
• RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains
• AAA rational approximation on a continuum