Geodesic metrics for RBF approximation of some physical quantities measured on sphere
Applications of Mathematics (2024)
- Volume: 69, Issue: 5, page 621-632
- ISSN: 0862-7940
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topSegeth, Karel. "Geodesic metrics for RBF approximation of some physical quantities measured on sphere." Applications of Mathematics 69.5 (2024): 621-632. <http://eudml.org/doc/299329>.
@article{Segeth2024,
abstract = {The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula. We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general.},
author = {Segeth, Karel},
journal = {Applications of Mathematics},
keywords = {spherical interpolation; radial basis function; spherical radial basis function; geodesic metric; trend; multiquadric; magnetic susceptibility},
language = {eng},
number = {5},
pages = {621-632},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Geodesic metrics for RBF approximation of some physical quantities measured on sphere},
url = {http://eudml.org/doc/299329},
volume = {69},
year = {2024},
}
TY - JOUR
AU - Segeth, Karel
TI - Geodesic metrics for RBF approximation of some physical quantities measured on sphere
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 5
SP - 621
EP - 632
AB - The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula. We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general.
LA - eng
KW - spherical interpolation; radial basis function; spherical radial basis function; geodesic metric; trend; multiquadric; magnetic susceptibility
UR - http://eudml.org/doc/299329
ER -
References
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