Regularized Least Squares Approximations on the Sphere Using Spherical Designs

DOI10.1137/110838601zbMath1253.65035OpenAlexW2088545848MaRDI QIDQ2903048

Xiaojun Chen, Robert S. Womersley, Congpei An, Ian H. Sloan

Publication date: 23 August 2012

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10397/6030

zbMATH Keywords

regularizationspherical designspherical harmonicserror boundquadrature formulaLaplace-Beltrami operatorleast squares problemspherical polynomialsfiltered approximationregularized least squares approximation

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical computation of solutions to systems of equations (65H10) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Spherical $t_\epsilon $-designs for approximations on the sphere ⋮ Fully discrete needlet approximation on the sphere ⋮ Spectral numerical exterior calculus methods for differential equations on radial manifolds ⋮ Radial basis function approximation of noisy scattered data on the sphere ⋮ Uniform approximation on the sphere by least squares polynomials ⋮ Least squares spherical harmonics approximation on the cubed sphere ⋮ A discrete Funk transform on the cubed sphere ⋮ Sketching with Spherical Designs for Noisy Data Fitting on Spheres ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions ⋮ Needlet approximation for isotropic random fields on the sphere ⋮ Filtered hyperinterpolation: a constructive polynomial approximation on the sphere ⋮ Continuous regularized least squares polynomial approximation on the sphere ⋮ Quadrature rules with neighborhood of spherical designs on the two-sphere ⋮ Fast cross-validation in harmonic approximation ⋮ Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere ⋮ On the quadrature exactness in hyperinterpolation ⋮ Lasso Hyperinterpolation Over General Regions ⋮ Distributing many points on spheres: minimal energy and designs

Uses Software

• QSHEP3D

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