Geodesic metrics for RBF approximation of some physical quantities measured on sphere
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599934" target="_blank" >RIV/67985840:_____/24:00599934 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.21136/AM.2024.0051-24" target="_blank" >https://doi.org/10.21136/AM.2024.0051-24</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2024.0051-24" target="_blank" >10.21136/AM.2024.0051-24</a>
Alternative languages
Result language
angličtina
Original language name
Geodesic metrics for RBF approximation of some physical quantities measured on sphere
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
1572-9109
Volume of the periodical
69
Issue of the periodical within the volume
5
Country of publishing house
DE - GERMANY
Number of pages
12
Pages from-to
621-632
UT code for WoS article
001306175200001
EID of the result in the Scopus database
2-s2.0-85203197509