Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 41 min ago
Peer-reviewedCC BYActa Numerica

Applications of AAA rational approximation

  • Yuji Nakatsukasa1
  • Lloyd Nicholas Trefethen2
  1. 1University of Oxford
  2. 2Harvard University
Open at sourceDOICite

Abstract

The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis. For example, rational functions enable strikingly effective methods for numerical differentiation and integration; interpolation of equispaced data; locating zeros, poles, and branch points; analytic continuation; computation of inverse functions; imputation of missing data; computation of nonlinear eigenvalues and resonances; model order reduction/reduced order modelling; solution of Wiener–Hopf and Hilbert transform problems; conformal mapping; and solution of the two-dimensional Laplace, biharmonic and Helmholtz equations. The paper also surveys various improvements and generalizations of the AAA algorithm that have developed since its original appearance in 2018.

Related

  1. Lower bounds in H2-rational approximation to Blaschke products
    Laurent Baratchart, Alexander Borichev, Sylvain Chevillard +2
    Research in the Mathematical SciencesPeer-reviewedCC BY 4.0Full textAnalysis & PDEsHAL
  2. Campana Rational Connectedness and Weak Approximation of Del Pezzo Orbifolds
    Saptarshi Dandapat
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  3. Weighted Laplace Spaces for Spectral Measures and Rational Approximation
    Stefan Jakobsson, Alice Kozakevicius, Stig Larsson
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Stable Rational Approximation of PDE Transfer Functions with H∞ Error Bounds
    Aleksandr Talitckii, Matthew M. Peet
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Mapping for Approximation: A Unified View of Rescaled, Variably Scaled and Rational Kernel Methods
    Stefano De Marchi
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@article{nakatsukasa2026applications,
  title = {{Applications of AAA rational approximation}},
  author = {Yuji Nakatsukasa and Lloyd Nicholas Trefethen},
  journal = {Acta Numerica},
  year = {2026},
  month = jun,
  doi = {10.1017/s0962492925100263},
  url = {https://doi.org/10.1017/s0962492925100263},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Applications of AAA rational approximation
AU  - Yuji Nakatsukasa
AU  - Lloyd Nicholas Trefethen
PY  - 2026
DA  - 2026/06/19
JO  - Acta Numerica
DO  - 10.1017/s0962492925100263
UR  - https://doi.org/10.1017/s0962492925100263
AB  - The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis. For example, rational functions enable strikingly effective methods for numerical differentiation and integration; interpolation of equispaced data; locating zeros, poles, and branch points; analytic continuation; computation of inverse functions; imputation of missing data; computation of nonlinear eigenvalues and resonances; model order reduction/reduced order modelling; solution of Wiener–Hopf and Hilbert transform problems; conformal mapping; and solution of the two-dimensional Laplace, biharmonic and Helmholtz equations. The paper also surveys various improvements and generalizations of the AAA algorithm that have developed since its original appearance in 2018.
SN  - 0962-4929
SN  - 1474-0508
ER  -