Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the \(D_4\) symmetry group; interpolation within a squircle. I
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Publication:348664
DOI10.1016/j.jcp.2013.11.014zbMath1349.65056OpenAlexW2045467508MaRDI QIDQ348664
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2013.11.014
Chebyshev polynomialsdihedral groupradial basis functionsgroup theorypseudospectralZernike polynomials\(D_4\)
Related Items (9)
Correcting Three Errors in Kantorovich & Krylov′s <em>Approximate Methods of Higher Analysis</em> ⋮ Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions ⋮ Stable, fast computation of high-order Zernike moments using a recursive method ⋮ Regularized symmetric positive definite matrix factorizations for linear systems arising from RBF interpolation and differentiation ⋮ Spectral methods in non-tensor geometry. II: Chebyshev versus Zernike polynomials, gridding strategies and spectral extension on squircle-bounded and perturbed-quadrifolium domains ⋮ A new constructive and elementary proof of a Bernstein-Walsh theorem, improved to infinite order convergence, for functions \(C^\infty\) in an intricate but smooth two-dimensional real domain ⋮ Adaptive radial basis function and Hermite function pseudospectral methods for computing eigenvalues of the prolate spheroidal wave equation for very large bandwidth parameter ⋮ Approximation on non-tensor domains including squircles. III: Polynomial hyperinterpolation and radial basis function interpolation on Chebyshev-like grids and truncated uniform grids ⋮ The automatic solution of partial differential equations using a global spectral method
Uses Software
Cites Work
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- Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions
- Sparse generalized Fourier transforms
- Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform
- Error saturation in Gaussian radial basis functions on a finite interval
- Symmetry, groups, and boundary value problems. A progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry
- An analytical and numerical study of the two-dimensional Bratu equation
- A group-theoretic approach to computational bifurcation problems with symmetry
- On the possible application of group representations to some boundary value and eigenvalue problems of certain domains without classical symmetry. I: Domains \(D_N\) of the first type
- On the possible application of group representations to some boundary value and eigenvalue problems of certain domains without classical symmetry. II: Domains \(S_N\) of the second type and \(S_{N+(1/2)}\) of the third type
- Radial basis function approximation methods with extended precision floating point arithmetic
- Applications of the generalized Fourier transform in numerical linear algebra
- Eigenvalues for equivariant matrices
- Boundary Value Problems with Symmetry and Their Approximation by Finite Elements
- On group Fourier analysis and symmetry preserving discretizations of PDEs
- Scattered Data Approximation
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