Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems

DOI10.3103/S1066369X10030084zbMath1205.65346OpenAlexW2026518668MaRDI QIDQ1956590

A. A. Shomanova, S. S. Kudaibergenov, Nurlan Temirgaliyev

Publication date: 23 September 2010

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x10030084

zbMATH Keywords

sparse gridgeneralized Sobolev spacefunction spaces of dominating mixed smoothnesscomputation of Fourier coefficientsapproximate recoveryfinite Fourier sumgeneralized Korobov spacemultivariate periodic functionSmolyak quadrature formula

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier series and coefficients in several variables (42B05)

Related Items (7)

Orderly exact calculation of integrals of products of functions by the method of tensor products of functionals ⋮ General algorithm for the numerical integration of functions of several variables ⋮ On optimal discretization of solutions of the heat equation and the limit error of the optimum computing unit ⋮ Approximative capabilities of ``Smolyak type computational aggregates with Dirichlet, Fejér and Vallée-Poussin kernels in the scale of Ul'yanov classes ⋮ An exact order of discrepancy of the Smolyak grid and some general conclusions in the theory of numerical integration ⋮ Discretization of solutions to Poisson’s equation in the Korobov class ⋮ Computational (numerical) diameter in a context of general theory of a recovery

Cites Work

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• On the informativeness of linear functionals.
• On approximate recovery of functions with bounded mixed derivative
• An application of tensor products of functionals in problems of numerical integration
• Informativeness of all the linear functionals in the recovery of functions in the classes $ H_p^\omega$

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