A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm
DOI10.1137/21M1410580MaRDI QIDQ5087102
Kateryna Pozharska, Tino Ullrich
Publication date: 8 July 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.11124
rate of convergencereproducing kernel Hilbert spaceuniform normweighted least squaresrandom informationsampling recovery
Analysis of algorithms (68W40) Trigonometric approximation (42A10) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Sampling theory in information and communication theory (94A20)
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- Optimal approximation of multivariate periodic Sobolev functions in the sup-norm
- Mercer's theorem on general domains: on the interaction between measures, kernels, and RKHSs
- Tractability of multivariate problems. Volume III: Standard information for operators
- Breaking the curse for uniform approximation in Hilbert spaces via Monte Carlo methods
- Sampling, Marcinkiewicz-Zygmund inequalities, approximation, and quadrature rules
- Approximation of mixed order Sobolev functions on the \(d\)-torus: asymptotics, preasymptotics, and \(d\)-dependence
- Multivariate \(L_{\infty}\) approximation in the worst case setting over reproducing kernel Hilbert spaces
- Tractability of multivariate problems. Volume I: Linear information
- Regularity and approximability of electronic wave functions
- On the power of standard information for multivariate approximation in the worst case setting
- Polynomial interpolation results in Sobolev spaces
- The Kadison-Singer problem in discrepancy theory.
- Ismagilov type theorems for linear, Gel'fand and Bernstein \(n\)-widths
- Function values are enough for \(L_2\)-approximation. II
- How anisotropic mixed smoothness affects the decay of singular numbers for Sobolev embeddings
- Lower bounds for the error of quadrature formulas for Hilbert spaces
- On optimal recovery in \(L_2\)
- \(L_2\)-norm sampling discretization and recovery of functions from RKHS with finite trace
- A new upper bound for sampling numbers
- On the worst-case error of least squares algorithms for \(L_2\)-approximation with high probability
- Function values are enough for \(L_2\)-approximation
- Worst-case recovery guarantees for least squares approximation using random samples
- Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices
- Interlacing families. II: Mixed characteristic polynomials and the Kadison-Singer problem
- On approximate recovery of functions with bounded mixed derivative
- Exponential frames on unbounded sets
- Support Vector Machines
- LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
- Orthogonal polynomials
- Optimal weighted least-squares methods
- New Preasymptotic Estimates for Approximation of Periodic Sobolev Functions
- Pipage Rounding, Pessimistic Estimators and Matrix Concentration
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