On the ill-conditioned nature of \(C^\infty\) RBF strong collocation
type: Item
instance of: scholarly article
title: On the ill-conditioned nature of \(C^\infty\) RBF strong collocation
zbMATH Open document ID: 1403.65160
author: Pavel Holoborodko
author: E. J. Kansa
published in: Engineering Analysis with Boundary Elements
publication date: 2018-08-09T00:00:00Z
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 6915425
zbMATH Keywords: meshless radial basis functions
zbMATH Keywords: multiquadrics
zbMATH Keywords: Gaussians
zbMATH Keywords: partial differential equations
zbMATH Keywords: integralequations
zbMATH Keywords: multi-precision tools
MaRDI profile type: Publication
full work available at URL: j.enganabound.2017.02.006
OpenAlex ID: W2594409123
cites work: Q4716273
cites work: Multiquadric Prewavelets on Nonequally Spaced Knots in One Dimension
cites work: Analytic wavelets generated by radial functions
cites work: Q3973499
cites work: Multivariate Interpolation and Conditionally Positive Definite Functions. II
cites work: Miscellaneous error bounds for multiquadric and related interpolators
cites work: Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
cites work: Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
cites work: Error estimates and condition numbers for radial basis function interpolation
cites work: Preconditioning for radial basis functions with domain decomposition methods
cites work: Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method
cites work: Multiquadric and its shape parameter -- a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation
cites work: More accuracy at fixed precision.
cites work: Error bounds from extra-precise iterative refinement
cites work: Scattered Data Interpolation: Tests of Some Method
cites work: The shape parameter in the shifted surface spline. III.
cites work: The mystery of the shape parameter. III
cites work: Numerical solution to time-dependent 4D inviscid Burgers' equations
DOI: 10.1016/J.ENGANABOUND.2017.02.006
description: scientific article; zbMATH DE number 6915425