Sigmoid functions, multiscale resolution of singularities, and \(hp\)-mesh refinement
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Publication:6636580
DOI10.1137/23M1556629MaRDI QIDQ6636580
Daan Huybrechs, Lloyd N. Trefethen
Publication date: 12 November 2024
Published in: SIAM Review (Search for Journal in Brave)
rational approximationradial basis functionsigmoid functionlogistic function\(hp\)-mesh refinementDE quadraturegeneralized Gauss quadrature
Approximation by rational functions (41A20) Algorithms for approximation of functions (65D15) Numerical quadrature and cubature formulas (65D32)
Cites Work
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- Universal quadratures for boundary integral equations on two-dimensional domains with corners
- The h-p version of the finite element method. I. The basic approximation results
- On optimal global error bounds obtained by scaled local error estimates
- Approximation by superposition of sigmoidal and radial basis functions
- Double exponential formulas for numerical integration
- Poles and zeros of best rational approximants of \(| x|\)
- On the approximation of functions.
- Interpolation in the limit of increasingly flat radial basis functions
- Multilayer feedforward networks are universal approximators
- Representation of conformal maps by rational functions
- The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
- \(hp\)-finite element methods for singular perturbations
- Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
- Rational approximation to \(|x|\)
- Saint-Venant's principle
- A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
- Approximation by Polynomials with Locally Geometric Rates
- On the Gibbs Phenomenon and Its Resolution
- Radial Basis Functions
- New Laplace and Helmholtz solvers
- Solving Laplace Problems with Corner Singularities via Rational Functions
- Filters, mollifiers and the computation of the Gibbs phenomenon
- Lightning Stokes Solver
- Approximation by superpositions of a sigmoidal function
- The double-exponential transformation in numerical analysis
- A Padé-based algorithm for overcoming the Gibbs phenomenon
- The use of rational functions in numerical quadrature
- Resolution of Singularities by Rational Functions
- Numerical analytic continuation
- Computation of two-dimensional Stokes flows via lightning and AAA rational approximation
- Multivariate rational approximation of functions with curves of singularities
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