Spherical basis function approximation with particular trend functions

0571091 - MÚ 2024 RIV CZ eng C - Conference Paper (international conference)
Segeth, Karel
Spherical basis function approximation with particular trend functions.
Programs and Algorithms of Numerical Mathematics 21. Vol. 21. Prague: Institute of Mathematics CAS, 2023 - (Chleboun, J.; Kůs, P.; Papež, J.; Rozložnı́k, M.; Segeth, K.; Šı́stek, J.), s. 219-228. ISBN 978-80-85823-73-8.
[Programs and Algorithms of Numerical Mathematics /21./. Jablonec nad Nisou (CZ), 19.06.2022-24.06.2022]
Institutional support: RVO:67985840
Keywords : spherical interpolation * spherical radial basis function * inverse multiquadric
OECD category: Applied mathematics
http://dx.doi.org/10.21136/panm.2022.20

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.
Permanent Link: https://hdl.handle.net/11104/0342395