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06/23/2023
Computation of 2D Stokes flows via lightning and AAA rational approximation
Low Reynolds number fluid flows are governed by the Stokes equations. In...
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05/05/2023
AAA rational approximation on a continuum
AAA rational approximation has normally been carried out on a discrete s...
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03/03/2023
Sigmoid functions and multiscale resolution of singularities
In this short, conceptual paper we observe that essentially the same mat...
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02/06/2023
Resolution of singularities by rational functions
Results on the rational approximation of functions containing singularit...
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08/08/2022
Spectacularly large expansion coefficients in Müntz's theorem
Müntz's theorem asserts, for example, that the even powers 1, x^2, x^4,…...
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07/24/2022
AAA interpolation of equispaced data
We propose AAA rational approximation as a method for interpolating or a...
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12/27/2021
Rectangular eigenvalue problems
Often the easiest way to discretize an ordinary or partial differential ...
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07/04/2021
AAA-least squares rational approximation and solution of Laplace problems
A two-step method for solving planar Laplace problems via rational appro...
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07/04/2021
Lightning Stokes solver
Gopal and Trefethen recently introduced "lightning solvers" for the 2D L...
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01/23/2021
Exactness of quadrature formulas
The standard design principle for quadrature formulas is that they shoul...
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10/05/2020
Reciprocal-log approximation and planar PDE solvers
This article is about both approximation theory and the numerical soluti...
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07/23/2020
Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
Rational approximations of functions with singularities can converge at ...
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11/22/2019
Vandermonde with Arnoldi
Vandermonde matrices are exponentially ill-conditioned, rendering the fa...
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11/09/2019
Numerical conformal mapping with rational functions
New algorithms are presented for numerical conformal mapping based on ra...
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08/29/2019
Quantifying the ill-conditioning of analytic continuation
Analytic continuation is ill-posed, but becomes merely ill-conditioned (...
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08/16/2019
An algorithm for real and complex rational minimax approximation
Rational minimax approximation of real functions on real intervals is an...
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05/08/2019