Recovery of Sobolev functions restricted to iid sampling

DOI10.1090/mcom/3763OpenAlexW3192515875WikidataQ113823079 ScholiaQ113823079MaRDI QIDQ5103756

Erich Novak, Mathias Sonnleitner, David Krieg

Publication date: 8 September 2022

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.02055

zbMATH Keywords

rate of convergencenumerical integrationoptimal recoveryrandom informationinterior cone condition

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Algorithms for approximation of functions (65D15) Complexity and performance of numerical algorithms (65Y20) Numerical integration (65D30)

Related Items (2)

A sharp upper bound for sampling numbers in \(L_2\) ⋮ Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tractability of multivariate problems. Volume III: Standard information for operators
• Randomized approximation of Sobolev embeddings. II
• Randomized approximation of Sobolev embeddings. III
• Function spaces in Lipschitz domains and optimal rates of convergence for sampling
• Random approximation of Sobolev embeddings
• Deterministic and stochastic error bounds in numerical analysis
• Optimal Monte Carlo methods for \(L^2\)-approximation
• Function values are enough for \(L_2\)-approximation. II
• Hyperbolic cross approximation. Lecture notes given at the courses on constructive approximation and harmonic analysis, Barcelona, Spain, May 30 -- June 3, 2016
• Algorithms and complexity for functions on general domains
• Faster estimates of the mean of bounded random variables
• Solvable integration problems and optimal sample size selection
• On optimal recovery in \(L_2\)
• Optimal pointwise sampling for \(L^2\) approximation
• Stable high-order randomized cubature formulae in arbitrary dimension
• On the power of standard information for tractability for \(L_2\)-approximation in the average case setting
• 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
• Optimal Monte Carlo integration on closed manifolds
• Optimal confidence for Monte Carlo integration of smooth functions
• Mean estimation and regression under heavy-tailed distributions: A survey
• On the approximate calculation of multiple integrals
• A universal algorithm for multivariate integration
• Local polynomial reproduction and moving least squares approximation
• Multilevel Monte Carlo Methods
• 4. On the power of random information
• Support Vector Machines
• Polynomial Approximation of Functions in Sobolev Spaces
• The Covering Radius of Randomly Distributed Points on a Manifold
• Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
• Random sections of ellipsoids and the power of random information
• A Monte Carlo Method for Integration of Multivariate Smooth Functions
• Understanding Machine Learning
• Sobolev Spaces
• Scattered Data Approximation

This page was built for publication: Recovery of Sobolev functions restricted to iid sampling