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Applications of AAA rational approximation
Part of:
Partial differential equations, boundary value problems
Series expansions
Numerical approximation and computational geometry
Approximations and expansions
Published online by Cambridge University Press: 19 June 2026
Abstract
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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.
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