Sampling and cubature on sparse grids based on a B-spline quasi-interpolation
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Publication:515985
DOI10.1007/s10208-015-9274-8zbMath1359.41001arXiv1211.4319OpenAlexW76303595MaRDI QIDQ515985
Publication date: 17 March 2017
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1211.4319
sparse gridscubature formulasB-spline quasi-interpolation representationsBesov-type spaces of anisotropic smoothnesslinear sampling algorithmsoptimal cubatureoptimal sampling recovery
Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)
Related Items (17)
Approximation of functions with small mixed smoothness in the uniform norm ⋮ Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in \(H^\gamma\) ⋮ Optimization of black-box problems using Smolyak grids and polynomial approximations ⋮ Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness ⋮ Optimal sampling recovery of mixed order Sobolev embeddings via discrete {L}ittlewood--{P}aley type characterizations ⋮ Rate-optimal sparse approximation of compact break-of-scale embeddings ⋮ Deep ReLU neural networks in high-dimensional approximation ⋮ B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness ⋮ Sparse grid approximation in weighted Wiener spaces ⋮ Adaptive sampling recovery of functions with bounded modulus of smoothness ⋮ Quasi-interpolation representation and sampling recovery of multivariate functions ⋮ Approximation by translates of a single function of functions in space induced by the convolution with a given function ⋮ Dimension-dependent error estimates for sampling recovery on Smolyak grids based on B-spline quasi-interpolation ⋮ Sampling numbers of a class of infinitely differentiable functions ⋮ Sample numbers and optimal Lagrange interpolation of Sobolev spaces \(W_1^r\) ⋮ Local and global phaseless sampling in real spline spaces ⋮ A higher order Faber spline basis for sampling discretization of functions
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