Optimal cubature formulas for tensor products of certain classes of functions

DOI10.1016/j.jco.2011.01.001zbMath1231.41029OpenAlexW2076055114MaRDI QIDQ647923

Dmytro S. Skorokhodov, Sergiy V. Borodachov, Vladislav F. Babenko

Publication date: 21 November 2011

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2011.01.001

zbMATH Keywords

Sobolev spacemodulus of continuitytensor productoptimal quadrature formulasworst-case errorsoptimal cubature in the worst-case setting

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction of optimal cubature formulas related to computer tomography
• Tractability of multivariate problems. Volume I: Linear information
• Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives
• Widths and best quadrature formulas for convolution classes
• Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions
• Exact inequalities for splines and best quadrature formulas for certain classes of functions
• Faithful asymptotics of remainders optimal for some classes of functions with cubic weight formulas
• On the optimal error bound for cubature formulae on certain classes of continuous functions
• Cubature formulas, discrepancy, and nonlinear approximation
• Cubature formulae for spheres, simplices and balls.
• Uniqueness of the Gaussian quadrature for a ball
• Sampling, wavelets and tomography.
• On the construction of optimal cubature formulae which use integrals over hyperspheres
• On the best interval quadrature formulae for classes of differentiable periodic functions
• Best cubature formulas for some classes of functions of many variables
• Quadrature formulas with minimum error for certain classes of functions
• Gaussian extended cubature formulae for polyharmonic functions
• Monosplines of minimal norm and the best quadrature formulae
• Quadrature formulae and recovery of number-theoretical nets from nodal values for classes of functions with small degree of smoothness
• ON THE BEST QUADRATURE FORMULA OF THE FORM $ \sum_{k=1}^np_kf(x_k)$ FOR SOME CLASSES OF DIFFERENTIABLE PERIODIC FUNCTIONS
• BEST QUADRATURE FORMULA FOR SOME CLASSES OF PERIODIC DIFFERENTIABLE FUNCTIONS
• On optimization of weight quadrature formulas
• Some problems in approximation theory and numerical analysis
• Integration of polyharmonic functions
• Optimal quadrature formulae
• Best Approximate Integration Formulas; Best Approximation Formulas
• Investigation of the optimization of quadrature formulas by Dnepropetrovsk mathematicians
• An extension of the Pizzetti formula for polyharmonic functions

This page was built for publication: Optimal cubature formulas for tensor products of certain classes of functions