Regularized kernel-based reconstruction in generalized Besov spaces
DOI10.1007/s10208-017-9346-zzbMath1392.41008OpenAlexW2611021540MaRDI QIDQ1750389
Christian Rieger, Barbara Zwicknagl, Michael Griebel
Publication date: 18 May 2018
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10208-017-9346-z
reproducing kernelsa priori error analysisspline smoothinggeneralized Besov spacesfeasible reconstruction schemes
Nonparametric regression and quantile regression (62G08) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Positive definite functions in one variable harmonic analysis (42A82) Rate of convergence, degree of approximation (41A25) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held May 5--11, 2013.
- Extension of sampling inequalities to Sobolev semi-norms of fractional order and derivative data
- Minimum Sobolev norm interpolation with trigonometric polynomials on the torus
- Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds
- \(L^p\) Bernstein inequalities and inverse theorems for RBF approximation on \(\mathbb{R}^d\)
- \(n\)-parameter families and best approximation
- Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning
- Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
- Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions
- An estimate for multivariate interpolation. II
- Decomposition of spaces of distributions induced by Hermite expansions
- Eignets for function approximation on manifolds
- Estimates for functions in Sobolev spaces defined on unbounded domains
- Convergence rates for multivariate smoothing spline functions
- Random walks on graphs with regular volume growth
- Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold
- Heat kernel generated frames in the setting of Dirichlet spaces
- The covering number in learning theory
- Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions
- Diffusion polynomial frames on metric measure spaces
- An extension of a bound for functions in Sobolev spaces, with applications to \((m, s)\)-spline interpolation and smoothing
- Tight frame expansions of multiscale reproducing kernels in Sobolev spaces
- Multiscale kernels
- Approximate interpolation with applications to selecting smoothing parameters
- Local polynomial reproduction and moving least squares approximation
- Inverse and saturation theorems for radial basis function interpolation
- Hilbert space embeddings and metrics on probability measures
- Kernel Approximation on Manifolds II: The $L_{\infty}$ Norm of the $L_2$ Projector
- On Haar's Theorem Concerning Chebychev Approximation Problems Having Unique Solutions
- Learning Theory
- Localized Tight Frames on Spheres
- Kernel techniques: From machine learning to meshless methods
- Frames and factorization of graph Laplacians
- $L^p$ Bernstein estimates and approximation by spherical basis functions
- ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY
- A sampling theorem on homogeneous manifolds
- An inverse theorem for compact Lipschitz regions in ℝ^{𝕕} using localized kernel bases
- Scattered-Data Interpolation on $\bb R^\protectn$: Error Estimates for Radial Basis and Band-Limited Functions
- Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
- Dimensions, Whitney covers, and tubular neighborhoods
- Sampling and Stability
- Multiscale Approximation and Reproducing Kernel Hilbert Space Methods
- Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
- Scattered Data Approximation
This page was built for publication: Regularized kernel-based reconstruction in generalized Besov spaces