Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere

DOI10.1137/140964990zbMath1314.65040arXiv1501.02090OpenAlexW1988680074MaRDI QIDQ5253576

Pavlo Tkachenko, Ian H. Sloan, Sergei V. Pereverzyev

Publication date: 27 May 2015

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

Full work available at URL: https://arxiv.org/abs/1501.02090

zbMATH Keywords

regularizationpenalizationspherical polynomialparameter choice strategya posteriori rulescontinuous function on sphere

Mathematics Subject Classification ID

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

Related Items (9)

Spherical $t_\epsilon $-designs for approximations on the sphere ⋮ \(L_2\) error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data ⋮ Lasso trigonometric polynomial approximation for periodic function recovery in equidistant points ⋮ Parameter choice strategies for error expressions and the numerical stability of Tikhonov-regularized approximation formulae ⋮ Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions ⋮ Tikhonov regularization for polynomial approximation problems in Gauss quadrature points ⋮ Continuous regularized least squares polynomial approximation on the sphere ⋮ Fast cross-validation in harmonic approximation ⋮ Lasso Hyperinterpolation Over General Regions

Uses Software

• QSHEP3D
• chammp

Cites Work

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