scientific article; zbMATH DE number 1049042
From MaRDI portal
Publication:4348451
zbMath0899.41001MaRDI QIDQ4348451
Publication date: 17 August 1997
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Approximation by polynomials (41A10) Algorithms for approximation of functions (65D15) Research exposition (monographs, survey articles) pertaining to approximations and expansions (41-02)
Related Items
Approximation of functions with small mixed smoothness in the uniform norm, Gelfand numbers of embeddings of mixed Besov spaces, \(s\)-numbers of embeddings of weighted Wiener algebras, Kolmogorov widths of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables in the space \(L_q\), On optimal approximation in periodic Besov spaces, A new upper bound for sampling numbers, On generation and enumeration of orthogonal Chebyshev-Frolov lattices, Fast computation of the multidimensional discrete Fourier transform and discrete backward Fourier transform on sparse grids, Univariate modified Fourier methods for second order boundary value problems, On the Sidon inequality for trigonometric polynomials, Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications, Fast discrete algorithms for sparse Fourier expansions of high dimensional functions, Pointwise multipliers for Sobolev and Besov spaces of dominating mixed smoothness, Change of variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit cube, On shrinking minimax convergence in nonparametric statistics, Approximation in periodic Gevrey spaces, Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness, A universal algorithm for multivariate integration, On filtered polynomial approximation on the sphere, Connections between numerical integration, discrepancy, dispersion, and universal discretization, Counting Via Entropy: New Preasymptotics for the Approximation Numbers of Sobolev Embeddings, Approximation by classical orthogonal polynomials with weight in spaces \(L_{2, \gamma }(a,b)\) and widths of some functional classes, Exact asymptotic orders of various randomized widths on Besov classes, Incremental Greedy Algorithm and Its Applications in Numerical Integration, On “Upper Error Bounds for Quadrature Formulas on Function Classes” by K.K. Frolov, Some trigonometric polynomials with extremely small uniform norm and their applications, Optimal cubature formulas in weighted Besov spaces with \(A _{\infty }\) weights on multivariate domains, Representation of polynomials by linear combinations of radial basis functions, Wavelet approximation and Fourier widths of classes of periodic functions of several variables. II, On the widths of Sobolev classes, Exponential tractability of \(L_2\)-approximation with function values, Estimates of the best orthogonal trigonometric approximations and orthoprojective widths of the classes of periodic functions of many variables in a uniform metric, Randomized approximation numbers on Besov classes with mixed smoothness, Linear and Kolmogorov widths of the classes \(B_{p,\theta}^{\Omega}\) of periodic functions of one and several variables, New Preasymptotic Estimates for Approximation of Periodic Sobolev Functions, Minimax goodness-of-fit testing in multivariate nonparametric regression, Best approximations of periodic functions of several variables from the classes \(B_{p,\theta}^{\Omega}\), Estimates of the Fourier widths of classes of Nikol'skii-Besov and Lizorkin-Triebel types of periodic functions of several variables, Approximation of classes \(B_{p,\theta}^r\) of periodic functions of one and several variables, \(N\)-widths and \(\varepsilon \)-dimensions for high-dimensional approximations, Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions, Approximation rates for the hierarchical tensor format in periodic Sobolev spaces, Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square, Approximation numbers of Sobolev embeddings-sharp constants and tractability, Intractability results for positive quadrature formulas and extremal problems for trigonometric polynomials, Estimates of the values of \(n\)-widths of classes of analytic functions in the weight spaces \(H_{2,\gamma}(D)\), On the entropy numbers between the anisotropic spaces and the spaces of functions with mixed smoothness, Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol'skii-Besov spaces, Interpolation and integral norms of hyperbolic polynomials, Multivariate Modified Fourier Expansions, Isotropic and dominating mixed Besov spaces: A comparison, Function values are enough for \(L_2\)-approximation, Function values are enough for \(L_2\)-approximation. II, High dimensional numerical problems, Worst-case recovery guarantees for least squares approximation using random samples, Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms, Efficient multivariate approximation on the cube, 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, Multivariate approximation by translates of the Korobov function on Smolyak grids, Representation and \(m\)-term approximation for anisotropic Besov classes, Best bilinear approximations for the classes of functions of many variables, Approximation of the classes \(H_p^\omega\) of periodic functions of many variables in the space \(L_p\), On the problem of linear widths of the classes \(B_{p,\theta}^r\) of periodic functions of many variables, Embeddings for infinite-dimensional integration and \(L_2\)-approximation with increasing smoothness, Optimal approximation of elliptic problems by linear and nonlinear mappings. II, Approximate characteristics of the classes \({B}_{p,\theta}^{\Omega}\) of periodic functions of one variable and many ones, The Role of Frolov's Cubature Formula for Functions with Bounded Mixed Derivative, Almost periodic functions and their applications: a survey of results and perspectives, Computational (numerical) diameter in a context of general theory of a recovery, Hyperbolic wavelet analysis of classical isotropic and anisotropic Besov-Sobolev spaces, Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces, On optimal recovery in \(L_2\), Greedy algorithms and Kolmogorov widths in Banach spaces, On \(N\) -termed approximations in \(H^s\)-norms with respect to the Haar system, Linear and nonlinear methods of relief approximation, Optimal query error of quantum approximation on some Sobolev classes, The information-based complexity of approximation problem by adaptive Monte Carlo methods, Convergence acceleration of modified Fourier series in one or more dimensions, Transformed rank-1 lattices for high-dimensional approximation, Integral norm discretization and related problems, On the estimates of widths of the classes of functions defined by the generalized moduli of continuity and majorants in the weighted space \(L_{2,x}(0, 1)\), Approximating characteristics of the classes of periodic multivariate functions in the space \(B_{ \infty , 1} \), Error Estimates for Multivariate Regression on Discretized Function Spaces, Tractable embeddings of Besov spaces into small Lebesgue spaces, Sparse Fourier transforms on rank-1 lattices for the rapid and low-memory approximation of functions of many variables, The best approximations and widths of the classes of periodical functions of one and several variables in the space \(B_{\infty, 1}\), Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices, A Class of Periodic Function Spaces and Interpolation on Sparse Grids, Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions, Generalized sparse grid interpolation based on the fast discrete Fourier transform, Estimates of the approximation characteristics of the classes \(B_{p,\theta}^\Omega\) of periodic functions of several variables with given majorant of mixed moduli of continuity, Estimation of some approximating characteristics of the classes of periodic functions of one and many variables, Greedy algorithm for functions with low mixed smoothness, Approximation of multivariate periodic functions by trigonometric polynomials based on sampling along rank-1 lattice with generating vector of Korobov form, Approximation by Fourier sums in the classes of Weyl-Nagy differentiable functions with high exponent of smoothness, Best orthogonal trigonometric approximations of the Nikol'skii-Besov-type classes of periodic functions in the space \(B_{ \infty ,1}\), Approximation of the classes of periodic functions of one and many variables from the Nikol'skii-Besov and Sobolev spaces, Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space \(B_{1,1}\), A Monte Carlo Method for Integration of Multivariate Smooth Functions, Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi‐continuous functions, Deep ReLU neural networks in high-dimensional approximation, Path regularity of the Brownian motion and the Brownian sheet, On the reconstruction of functions from values at subsampled quadrature points, Characteristics of the linear and nonlinear approximations of the Nikol'skii-Besov-type classes of periodic functions of several variables, Fast hyperbolic wavelet regression meets ANOVA, New lower bounds for the integration of periodic functions, Thresholding algorithms, maxisets and well-concentrated bases, Optimal algorithms for diagonal operators on N-widths in different computational setting, On the optimal convergence rate of universal and nonuniversal algorithms for multivariate integration and approximation, Numerical integration and discrepancy, a new approach, Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square, Fast Discrete Fourier Transform on Generalized Sparse Grids, Compactness properties of certain integral operators related to fractional integration, Kolmogorov and linear widths of weighted Besov classes, Order estimates of the \(L_q\)-norms of generalized derivatives of the Dirichlet-type kernels with an arbitrary choice of harmonics, Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in \(H^\gamma\), Optimal approximation of multivariate periodic Sobolev functions in the sup-norm, Approximation numbers of Sobolev and Gevrey type embeddings on the sphere and on the ball -- preasymptotics, asymptotics, and tractability, Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions, Hölder-Lipschitz norms and their duals on spaces with semigroups, with applications to earth mover's distance, Average sampling numbers of multivariate periodic function spaces with a Gaussian measure, Universal discretization, Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems, Trigonometric approximations and Kolmogorov widths of anisotropic Besov classes of periodic functions of several variables, Order estimates for the best approximations and approximations by Fourier sums in the classes of convolutions of periodic functions of low smoothness in the uniform metric, Sparse high-dimensional FFT based on rank-1 lattice sampling, Approximation and entropy numbers of embeddings between approximation spaces, On best \(m\)-term approximations and the entropy of sets in the space \(L^ 1\), An extrapolation theorem for nonlinear approximation and its applications, Estimates for bilinear approximations of the classes \(S_{p,\theta}^\Omega B\) of periodic functions of two variables, Approximation of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables by Fourier sums in the space \(L_p\) with \(p=1,\infty\), Approximation of infinitely differentiable multivariate functions is not strongly tractable, Spaces of functions of mixed smoothness and approximation from hyperbolic crosses, Estimate of approximate characteristics for classes of functions with bounded mixed derivative, Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I, On the orthogonality of the Chebyshev-Frolov lattice and applications, Order estimates for the best orthogonal trigonometric approximations of the classes of convolutions of periodic functions of low smoothness, On low discrepancy sequences and low discrepancy ergodic transformations of the multidimensional unit cube, A \(\varphi\)-transform result for spaces with dominating mixed smoothness properties, Optimal sampling recovery of mixed order Sobolev embeddings via discrete {L}ittlewood--{P}aley type characterizations, \(N\)-widths and average widths of Besov classes in Sobolev spaces, Nonlinear tensor product approximation of functions, Best approximation of periodic functions of several variables from the classes \( MB_{p,\theta}^\omega\), Optimal adaptive sampling recovery, Approximating characteristics of the classes \(L_{\beta,p}^\psi\) of periodic functions in the space \(L_q\), Order estimates for the best approximations and approximations by Fourier sums of the classes of \((\psi, \beta)\)-differential functions, On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_1\) or \(L_\infty\), Optimal recovery of Besov classes of generalized smoothness and Sobolev classes on the sphere, New explicit-in-dimension estimates for the cardinality of high-dimensional hyperbolic crosses and approximation of functions having mixed smoothness, Approximation of mixed order Sobolev functions on the \(d\)-torus: asymptotics, preasymptotics, and \(d\)-dependence, Cubature formulas, discrepancy, and nonlinear approximation, B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness, Nonlinear approximation of function spaces of mixed smoothness, Estimation of the entropy numbers and Kolmogorov widths for the Nikol'skii-Besov classes of periodic functions of many variables, Kolmogorov widths for analogs of the Nikol'skii-Besov classes with logarithmic smoothness, Approximations of the classes \(\mathbf{MB}_{p,\theta}^{r}\) of periodic functions of several variables by polynomials according to the Haar system, Wavelet approximation in weighted Sobolev spaces of mixed order with applications to the electronic Schrödinger equation, Widths of Besov classes of generalized smoothness on the sphere, Multiple rank-1 lattices as sampling schemes for multivariate trigonometric polynomials, B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness, Integration error for multivariate functions from anisotropic classes, Approximation by polynomials and ridge functions of classes of \(s\)-monotone radial functions, Estimates for widths of classes of periodic multivariable functions, Fibonacci sets and symmetrization in discrepancy theory, Kolmogorov widths between the anisotropic space and the space of functions with mixed smoothness, Entropy numbers and widths for the classes \(B_{p,\theta}^r\) of periodic functions of many variables, Best trigonometric and bilinear approximations for the classes of \((\psi,\beta)\)-differentiable periodic functions, Kolmogorov widths of the anisotropic Besov classes of periodic functions of many variables, Best \(m\)-term trigonometric approximation for periodic functions with low mixed smoothness from the Nikol'skii-Besov-type classes, Widths of the anisotropic Besov classes of periodic functions of several variables, Bernstein-Nikol'skii-type inequalities for trigonometric polynomials with an arbitrary choice of harmonics, A note on the dispersion of admissible lattices, The complexity of function approximation on Sobolev spaces with bounded mixed derivative by linear Monte Carlo methods, Widths between the anisotropic spaces and the spaces of functions with mixed smoothness, Approximation of multivariate periodic functions on the space with a Gaussian measure, Approximation of high-dimensional rank one tensors, Fast sparse nonlinear Fourier expansions of high dimensional functions, Lattice rules with random \(n\) achieve nearly the optimal \(\mathcal{O}(n^{-\alpha-1/2})\) error independently of the dimension, Weyl numbers of embeddings of tensor product Besov spaces, Preasymptotics and asymptotics of approximation numbers of anisotropic Sobolev embeddings, Digital net properties of a polynomial analogue of Frolov's construction, Strong summability of Fourier series and generalized Morrey spaces, Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices, Sampling and cubature on sparse grids based on a B-spline quasi-interpolation, On the entropy numbers of the mixed smoothness function classes, Best bilinear approximations of the classes \(S_{p,\theta}^\Omega B\) of periodic functions of many variables, Lower bound for quantum integration error on anisotropic Sobolev classes, A note on level-2 condition numbers, Multivariate modified Fourier series and application to boundary value problems, Computational complexity of the integration problem for anisotropic classes, Approximation of smooth functions on compact two-point homogeneous spaces, Approximation of functions in several variables from classes \(H^{\Omega}_p\) by polynomials with respect to the Haar system, Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness, Pointwise multipliers for Besov spaces of dominating mixed smoothness. II, Anisotropic smoothness classes: from finite element approximation to image models, Widths of weighted Sobolev classes on the ball, Some problems in the theory of ridge functions, Estimates for certain approximation characteristics of Nikol'skii-Besov spaces with generalized mixed smoothness, Smooth fixed volume discrepancy, dispersion, and related problems, Non-linear sampling recovery based on quasi-interpolant wavelet representations, Embedding of Lipschitz classes into classes of functions of \(\Lambda \)-bounded variation, The essential rate of approximation for radial function manifold, What Monte Carlo models can do and cannot do efficiently?, Approximation of \(MH_q^r\)-class functions by Haar polynomials, Optimal recovery on the classes of functions with bounded mixed derivative, Fast cross-validation in harmonic approximation, Interpolation of functions from Besov-type spaces on Gauß-Chebyshev grids, Learning a function from noisy samples at a finite sparse set of points, Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross, Wavelet characterizations for anisotropic Besov spaces, Universal bases and greedy algorithms for anisotropic function classes, Kolmogorov \(n\)-widths of function classes induced by a non-degenerate differential operator: a convex duality approach
