Multivariate Approximation

DOI10.1017/9781108689687zbMath1428.41001OpenAlexW4247119080MaRDI QIDQ4569637

Publication date: 27 June 2018

Full work available at URL: https://doi.org/10.1017/9781108689687

entropy widths sparse approximation cubature formulas approximate recovery anisotropic Sobolev and Nikolskii spaces approximation by univariate functions greedy aproximation hyperbolic cross approximations optimality of the trigonometric system

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Research exposition (monographs, survey articles) pertaining to approximations and expansions (41-02) Approximations and expansions (41Axx)

Related Items

Numerical integration and discrepancy under smoothness assumption and without it, Approximation of functions with small mixed smoothness in the uniform norm, Lebesgue-type inequalities in greedy approximation, Optimal cubature formulas on classes of periodic functions in several variables, Sampling discretization of integral norms of the hyperbolic cross polynomials, Application of Fourier truncation method to numerical differentiation for bivariate functions, Sampling discretization and related problems, Optimal recovery of functions from numerical information on them and limiting error of the optimal computing unit, A remark on entropy numbers, Connections between numerical integration, discrepancy, dispersion, and universal discretization, Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions, A sharp upper bound for sampling numbers in \(L_2\), Best \(n\)-term approximation of diagonal operators and application to function spaces with mixed smoothness, Random points are good for universal discretization, Deep ReLU neural networks in high-dimensional approximation, On the absolute convergence of Fourier series of functions of two variables in the space \(C^{1,\omega}\), A note on the degree of ill-posedness for mixed differentiation on the \(d\)-dimensional unit cube, Lower bounds for the Wiener norm in \(\mathbb{Z}_p^d\), Sampling discretization of integral norms and its application, Remarks on sampling discretization of integral norms of functions, Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables, On universal sampling recovery in the uniform norm, The minimal radius of Galerkin information for the problem of numerical differentiation, Sampling discretization error of integral norms for function classes with small smoothness, Numerical weighted integration of functions having mixed smoothness, Universal sampling discretization, On estimates of \(m\)-term approximations on classes of functions with bounded mixed derivative in the Lorentz space, Exponential tractability of \(L_2\)-approximation with function values, Fast and stable approximation of analytic functions from equispaced samples via polynomial frames, Sampling discretization of the uniform norm, EESTIMATES OF BEST APPROXIMATIONS OF FUNCTIONS WITH LOGARITHMIC SMOOTHNESS IN THE LORENTZ SPACE WITH ANISOTROPIC NORM, Estimates of the best approximations of the functions of the Nikol'skii-Besov class in the generalized space of Lorentz, Towards optimal sampling for learning sparse approximation in high dimensions, Function values are enough for \(L_2\)-approximation, Function values are enough for \(L_2\)-approximation. II, Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness, On the fixed volume discrepancy of the Fibonacci sets in the integral norms, How anisotropic mixed smoothness affects the decay of singular numbers for Sobolev embeddings, On the fixed volume discrepancy of the Korobov point sets, Sampling discretization error of integral norms for function classes, Regression in Tensor Product Spaces by the Method of Sieves, Estimates of efficiency for two methods of stable numerical summation of smooth functions, Dimension-dependent error estimates for sampling recovery on Smolyak grids based on B-spline quasi-interpolation, Almost periodic functions and their applications: a survey of results and perspectives, Sampling numbers of a class of infinitely differentiable functions, Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation, Entropy numbers and Marcinkiewicz-type discretization, On optimal recovery in \(L_2\), Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration, Sample numbers and optimal Lagrange interpolation of Sobolev spaces \(W_1^r\), Marcinkiewicz-type discretization of \(L^p\)-norms under the Nikolskii-type inequality assumption, Integral norm discretization and related problems, Sampling discretization of integral norms, Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions, Improved Recovery Guarantees and Sampling Strategies for TV Minimization in Compressive Imaging, Estimates for the deviations of integral operators in semilinear metric spaces and their applications