Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere

DOI10.1137/100814731zbMath1261.65066OpenAlexW2047569290MaRDI QIDQ4903741

Daniel Potts, Manuel Gräf, Gabriele Drauschke

Publication date: 24 January 2013

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/100814731

zbMATH Keywords

numerical examplesfast Fourier transformsreproducing kernel Hilbert spacesnonlinear conjugate gradient methodhalftoningleast squares functionalcontinuous-domain quantizationdiscrepancy functionalsminimizing an attraction-repulsion functionalquadrature error functionals

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Nonsmooth analysis (49J52) Numerical methods for discrete and fast Fourier transforms (65T50) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spherical harmonics (33C55) Methods of local Riemannian geometry (53B21)

Related Items (10)

Optimal configurations of lines and a statistical application ⋮ Consistency of probability measure quantization by means of power repulsion-attraction potentials ⋮ Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold ⋮ Asymptotic behavior of average \(L_p\)-discrepancies ⋮ A projection method on measures sets ⋮ Fast generation of 2-D node distributions for mesh-free PDE discretizations ⋮ A solution to the energy minimization problem constrained by a density function ⋮ Curve based approximation of measures on manifolds by discrepancy minimization ⋮ Distributing many points on spheres: minimal energy and designs ⋮ A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics

Uses Software

• Matlab
• NFFT
• NFFT3

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