Local error estimates for radial basis function interpolation of scattered data

1993 ◽  
Vol 13 (1) ◽  
pp. 13-27 ◽  
Author(s):  
ZONG-MIN WU ◽  
ROBERT SCHABACK
Keyword(s):  
Radial Basis Function ◽  
Error Estimates ◽  
Basis Function ◽  
Scattered Data ◽  
Local Error ◽  
Radial Basis Function Interpolation ◽  
Radial Basis ◽  
Interpolation Of Scattered Data

scholarly journals LOCAL RADIAL BASIS FUNCTION APPROXIMATION ON THE SPHERE

2008 ◽  
Vol 77 (2) ◽  
pp. 197-224 ◽  
Author(s):  
KERSTIN HESSE ◽  
Q. T. LE GIA
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Test ◽  
Local Error ◽  
Spherical Cap ◽  
Radial Basis Function Interpolation ◽  
Local Point ◽  
Radial Basis ◽  
Point Set ◽  
Radial Basis Function Approximation

AbstractIn this paper we derive local error estimates for radial basis function interpolation on the unit sphere $\mathbb {S}^2\subset \mathbb {R}^3$. More precisely, we consider radial basis function interpolation based on data on a (global or local) point set $X\subset \mathbb {S}^2$ for functions in the Sobolev space $H^s(\mathbb {S}^2)$ with norm $\|\cdot \|_s$, where s>1. The zonal positive definite continuous kernel ϕ, which defines the radial basis function, is chosen such that its native space can be identified with $H^s(\mathbb {S}^2)$. Under these assumptions we derive a local estimate for the uniform error on a spherical cap S(z;r): the radial basis function interpolant ΛXf of $f\in H^s(\mathbb {S}^2)$ satisfies $\sup _{\mathbf {x}\in S(\mathbf {z};r)} |f(\mathbf {x})-\Lambda _X f(\mathbf {x})| \leq c h^{(s-1)/2} \|f\|_{s}$, where h=hX,S(z;r) is the local mesh norm of the point set X with respect to the spherical cap S(z;r). Our proof is intrinsic to the sphere, and makes use of the Videnskii inequality. A numerical test illustrates the theoretical result.

Impulse Noise Removal Using Adaptive Radial Basis Function Interpolation

2016 ◽  
Vol 36 (3) ◽  
pp. 1192-1223 ◽  
Author(s):  
T. Veerakumar ◽  
Ravi Prasad K. Jagannath ◽  
Badri Narayan Subudhi ◽  
S. Esakkirajan
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Impulse Noise ◽  
Noise Removal ◽  
Radial Basis Function Interpolation ◽  
Impulse Noise Removal ◽  
Radial Basis

scholarly journals Solution of the quantum fluid dynamical equations with radial basis function interpolation

2000 ◽  
Vol 61 (5) ◽  
pp. 5967-5976 ◽  
Author(s):  
Xu-Guang Hu ◽  
Tak-San Ho ◽  
Herschel Rabitz ◽  
Attila Askar
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Dynamical Equations ◽  
Quantum Fluid ◽  
Radial Basis Function Interpolation ◽  
Radial Basis
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