Spherical basis function approximation with particular trend functions

@inProceedings{Segeth2023,
abstract = {The paper is concerned with the measurement of scalar physical quantities at nodes on the $(d-1)$-dimensional unit sphere surface in the $d$-dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider $d=3$. We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful in the interpretation of many physical measurements. We show an example concerned with the measurement of anisotropy of magnetic susceptibility having extensive applications in geosciences and present numerical difficulties connected with the high condition number of the matrix of the system defining the interpolation.},
author = {Segeth, Karel},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {spherical interpolation; spherical radial basis function; trend; inverse multiquadric; magnetic susceptibility},
location = {Prague},
pages = {219-228},
publisher = {Institute of Mathematics CAS},
title = {Spherical basis function approximation with particular trend functions},
url = {http://eudml.org/doc/298999},
year = {2023},
}

TY - CLSWK
AU - Segeth, Karel
TI - Spherical basis function approximation with particular trend functions
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 219
EP - 228
AB - The paper is concerned with the measurement of scalar physical quantities at nodes on the $(d-1)$-dimensional unit sphere surface in the $d$-dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider $d=3$. We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful in the interpretation of many physical measurements. We show an example concerned with the measurement of anisotropy of magnetic susceptibility having extensive applications in geosciences and present numerical difficulties connected with the high condition number of the matrix of the system defining the interpolation.
KW - spherical interpolation; spherical radial basis function; trend; inverse multiquadric; magnetic susceptibility
UR - http://eudml.org/doc/298999
ER -