Small errors imply large evaluation instabilities

DOI10.1007/s10444-023-10026-2zbMath1528.65010OpenAlexW4361294422MaRDI QIDQ6038830

Robert Schaback

Publication date: 3 May 2023

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-023-10026-2

zbMATH Keywords

interpolationcollocationKansa methodrecovery of functionsno free lunch theoremtrade-off principle

Mathematics Subject Classification ID

Numerical interpolation (65D05) Algorithms for approximation of functions (65D15) Numerical radial basis function approximation (65D12)

Related Items (1)

Energy-stable global radial basis function methods on summation-by-parts form

Cites Work

• Unnamed Item
• Interpolation and approximation in Taylor spaces
• Stable calculation of Gaussian-based RBF-FD stencils
• Stability of kernel-based interpolation
• A Newton basis for kernel spaces
• Multivariate interpolation of arbitrarily spaced data by moving least squares methods
• Convergence order estimates of meshless collocation methods using radial basis functions
• Solving partial differential equations by collocation using radial basis functions
• Meshless methods: An overview and recent developments
• Stable computation of multiquadric interpolants for all values of the shape parameter
• Near-optimal data-independent point locations for radial basis function interpolation
• Error estimates and condition numbers for radial basis function interpolation
• Direct meshless local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation
• A computational tool for comparing all linear PDE solvers
• On Leja sequences: some results and applications
• Error Estimates in Sobolev Spaces for Moving Least Square Approximations
• Local polynomial reproduction and moving least squares approximation
• On generalized moving least squares and diffuse derivatives
• Stable Computations with Gaussian Radial Basis Functions
• Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
• Sur certaines suites liées aux ensembles plans et leur application à la représentation conforme
• Kernel techniques: From machine learning to meshless methods
• The approximation power of moving least-squares
• Radial Basis Functions
• Survey of meshless and generalized finite element methods: A unified approach
• Barycentric Lagrange Interpolation
• Convergence rate of the data-independent $P$-greedy algorithm in kernel-based approximation
• Scattered Data Approximation
• All well-posed problems have uniformly stable and convergent discretizations

This page was built for publication: Small errors imply large evaluation instabilities