Spherical RBF interpolation employing particular geodesic metrics and trend functions

Segeth, Karel

  • Programs and Algorithms of Numerical Mathematics, page 149-158

Abstract

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The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient for its existence. Particular formulae with specified geodesic metrics, trend and SRBFs are then constructed and tested on a series of magnetic susceptibility examples. The results show that this interpolation is sufficiently robust in general.

How to cite

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Segeth, Karel. "Spherical RBF interpolation employing particular geodesic metrics and trend functions." Programs and Algorithms of Numerical Mathematics. 2025. 149-158. <http://eudml.org/doc/299965>.

@inProceedings{Segeth2025,
abstract = {The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient for its existence. Particular formulae with specified geodesic metrics, trend and SRBFs are then constructed and tested on a series of magnetic susceptibility examples. The results show that this interpolation is sufficiently robust in general.},
author = {Segeth, Karel},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {radial basis function; spherical interpolation; spherical radial basis function; geodesic metric; trend; multiquadric; magnetic susceptibility},
pages = {149-158},
title = {Spherical RBF interpolation employing particular geodesic metrics and trend functions},
url = {http://eudml.org/doc/299965},
year = {2025},
}

TY - CLSWK
AU - Segeth, Karel
TI - Spherical RBF interpolation employing particular geodesic metrics and trend functions
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2025
SP - 149
EP - 158
AB - The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient for its existence. Particular formulae with specified geodesic metrics, trend and SRBFs are then constructed and tested on a series of magnetic susceptibility examples. The results show that this interpolation is sufficiently robust in general.
KW - radial basis function; spherical interpolation; spherical radial basis function; geodesic metric; trend; multiquadric; magnetic susceptibility
UR - http://eudml.org/doc/299965
ER -

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