Numerical integration with polynomial exactness over a spherical cap

DOI10.1007/s10444-011-9187-2zbMath1256.65024OpenAlexW1996710757MaRDI QIDQ453552

Robert S. Womersley, Kerstin Hesse

Publication date: 27 September 2012

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-011-9187-2

zbMATH Keywords

numerical integrationnumerical examplesMarkov inequalitiespositive weightsequal weight rulespolynomial exactnessspherical capstensor product rules

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Integration on manifolds; measures on manifolds (58C35) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Spherical harmonics (33C55) Harmonic analysis and spherical functions (43A90) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (18)

Subperiodic trigonometric subsampling: A numerical approach ⋮ A parameter choice strategy for the inversion of multiple observations ⋮ Fully discrete needlet approximation on the sphere ⋮ Numerical hyperinterpolation over spherical triangles ⋮ On the Recovery of Core and Crustal Components of Geomagnetic Potential Fields ⋮ A Petrov–Galerkin RBF method for diffusion equation on the unit sphere ⋮ Spherical Framelets from Spherical Designs ⋮ A Petrov--Galerkin Kernel Approximation on the Sphere ⋮ Numerical hyperinterpolation over nonstandard planar regions ⋮ Polynomial approximation and quadrature on geographic rectangles ⋮ Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles ⋮ Complexity of numerical integration over spherical caps in a Sobolev space setting ⋮ On the unique reconstruction of induced spherical magnetizations ⋮ Tight framelets and fast framelet filter bank transforms on manifolds ⋮ On analysis of kernel collocation methods for spherical PDEs ⋮ On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere ⋮ Spherical Potential Theory: Tools and Applications ⋮ Joint Inversion of Multiple Observations

Uses Software

• OPQ

Cites Work

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