Spherical basis function approximation with particular trend functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00571091" target="_blank" >RIV/67985840:_____/23:00571091 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.21136/panm.2022.20" target="_blank" >http://dx.doi.org/10.21136/panm.2022.20</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/panm.2022.20" target="_blank" >10.21136/panm.2022.20</a>

Result language
angličtina
Original language name
Spherical basis function approximation with particular trend functions
Original language description
The paper is concerned with the measurement of scalar physical quantities at nodes on the $(d-1)$-dimensional unit sphere surface in the hbox{$d$-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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Programs and Algorithms of Numerical Mathematics 21
ISBN
978-80-85823-73-8
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
219-228
Publisher name
Institute of Mathematics CAS
Place of publication
Prague
Event location
Jablonec nad Nisou
Event date
Jun 19, 2022
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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