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Applications of AAA rational approximation
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DOI：10.1017/S0962492925100263.png)
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Abstract
En 中文
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.
Keywords:
41A20
65D15
30B40
65N35
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11.3
Papers:
89
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3.4K
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