On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms

DOI10.1007/s00211-011-0399-7zbMath1232.65045OpenAlexW2029671051MaRDI QIDQ652262

Daniel Potts, Manuel Gräf

Publication date: 14 December 2011

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-011-0399-7

zbMATH Keywords

spherical functionsconjugate gradient methodspherical harmonicsNewton methodspherical designsunit spherequadrature errornonequispaced fast spherical Fourier transformsnonlinear optimization methodsoptimization algorithms on Riemannian manifolds

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Numerical methods for discrete and fast Fourier transforms (65T50) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Harmonic analysis and spherical functions (43A90) Methods of local Riemannian geometry (53B21)

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Uses Software

• FFTW
• NFFT
• Healpix
• NFFT3

Cites Work

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• Probabilistic Marcinkiewicz-Zygmund inequalities on the rotation group
• Computational existence proofs for spherical \(t\)-designs
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• On the computation of nonnegative quadrature weights on the sphere
• A variational characterisation of spherical designs
• A survey on spherical designs and algebraic combinatorics on spheres
• Spherical codes and designs
• Distributing many points on a sphere
• Fast spherical Fourier algorithms.
• McLaren's improved snub cube and other new spherical designs in three dimensions
• Efficient reconstruction of functions on the sphere from scattered data
• Spherical harmonics
• Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
• The Geometry of Algorithms with Orthogonality Constraints
• Fast evaluation of quadrature formulae on the sphere
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Optimal Numerical Integration on a Sphere

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