AAA interpolation of equispaced data

2022/07/24 by Daan Huybrechs, Lloyd N. Trefethen, Huybrechs, Daan +1 · 4 citations
Computer Science · Engineering · Physics and Astronomy · #41A20 #65D05 #65D15 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2207.11807

openalex publication_date 2022/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced data samples. Although it is always better to approximate from large numbers of samples if they are available, whether equispaced or not, this method often performs impressively even when the sampling grid is fairly coarse. In most cases it gives more accurate approximations than other methods.

Cited by

• Applications of AAA rational approximation
• Generalized Fourier Series: An N log2(N) extension for aperiodic functions that eliminates Gibbs oscillations
• A kernel compression method for distributed-order fractional partial differential equations
• Two intriguing variants of the AAA algorithm for rational approximation

Related

• AAA rational approximation on a continuum
• Applications of AAA rational approximation
• Multivariate Rational Approximation of Scattered Data Using the p-AAA Algorithm
• The first five years of the AAA algorithm
• Two intriguing variants of the AAA algorithm for rational approximation