OPTIMAL LOWER ESTIMATES FOR THE WORST CASE CUBATURE ERROR AND THE APPROXIMATION BY HYPERINTERPOLATION OPERATORS IN THE SOBOLEV SPACE SETTING ON THE SPHERE

DOI10.1142/S0219691309003264zbMath1183.41033OpenAlexW2035737711MaRDI QIDQ5189978

He Ping Wang

Publication date: 11 March 2010

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219691309003264

zbMATH Keywords

Sobolev spacehyperinterpolation operatorsworst case cubature error

Mathematics Subject Classification ID

Rate of convergence, degree of approximation (41A25) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items (6)

On the norm of the hyperinterpolation operator on the \(d\)-dimensional cube ⋮ Optimal randomized quadrature for weighted Sobolev and Besov classes with the Jacobi weight on the ball ⋮ On filtered polynomial approximation on the sphere ⋮ \(L_2\) error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data ⋮ Complexity of Monte Carlo integration for Besov classes on the unit sphere ⋮ On the norm of the hyperinterpolation operator on the unit ball

Cites Work

• Unnamed Item
• Numerical integration over spheres of arbitrary dimension
• Fractional derivatives and best approximations
• Hyperinterpolation on the sphere at the minimal projection order
• Generalized hyperinterpolation on the sphere and the Newman-shapiro operators
• Approximation of smooth functions on compact two-point homogeneous spaces
• Constructive polynomial approximation on the sphere
• Quadrature in Besov spaces on the Euclidean sphere
• A lower bound for the worst-case cubature error on spheres of arbitrary dimension
• Weighted quadrature formulas and approximation by zonal function networks on the sphere
• Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
• Optimal lower bounds for cubature error on the sphere \(S^2\)
• Worst-case errors in a Sobolev space setting for cubature over the sphere S²
• On generalized hyperinterpolation on the sphere
• The uniform norm of hyperinterpolation on the unit sphere in an arbitrary number of dimensions

This page was built for publication: OPTIMAL LOWER ESTIMATES FOR THE WORST CASE CUBATURE ERROR AND THE APPROXIMATION BY HYPERINTERPOLATION OPERATORS IN THE SOBOLEV SPACE SETTING ON THE SPHERE