Sparse-grid sampling recovery and numerical integration of functions having mixed smoothness

Rate of convergence, degree of approximation (41A25) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Numerical integration (65D30)

Cites Work

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Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in \(H^\gamma\)
Sampling and cubature on sparse grids based on a B-spline quasi-interpolation
B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness
Linear vs. nonlinear algorithms for linear problems
Function spaces in Lipschitz domains and optimal rates of convergence for sampling
Bases in function spaces, sampling, discrepancy, numerical integration
Non-linear sampling recovery based on quasi-interpolant wavelet representations
Multiplicative estimates for integral norms of differentiable functions of several variables
Gaussian rules on unbounded intervals
Optimal sampling recovery of mixed order Sobolev embeddings via discrete {L}ittlewood--{P}aley type characterizations
B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness
Optimal order quadrature error bounds for infinite-dimensional higher-order digital sequences
Markov-Sonin Gaussian rule for singular functions
Hyperbolic cross approximation. Lecture notes given at the courses on constructive approximation and harmonic analysis, Barcelona, Spain, May 30 -- June 3, 2016
Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
High-dimensional integration on \(\mathbb{R}^d\), weighted Hermite spaces, and orthogonal transforms
Integration in Hermite spaces of analytic functions
On approximate recovery of functions with bounded mixed derivative
Pointwise multipliers for Sobolev and Besov spaces of dominating mixed smoothness
A sharp upper bound for sampling numbers in \(L_2\)
Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness
Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
Multivariate Approximation
On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness
Weighted Polynomial Approximation and Numerical Methods for Integral Equations
Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
Sparse grids
High-dimensional integration: The quasi-Monte Carlo way
Sampling numbers of smoothness classes via \(\ell^1\)-minimization
Random points are good for universal discretization
Numerical weighted integration of functions having mixed smoothness
Optimal numerical integration and approximation of functions on \(\mathbb{R}^d\) equipped with Gaussian measure

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