Original title:
Spherical basis function approximation with particular trend functions
Authors:
Segeth, Karel Document type: Papers Conference/Event: Programs and Algorithms of Numerical Mathematics /21./, Jablonec nad Nisou (CZ), 20220619
Year:
2023
Language:
eng Abstract:
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.
Keywords:
inverse multiquadric; spherical interpolation; spherical radial basis function Host item entry: Programs and Algorithms of Numerical Mathematics 21, ISBN 978-80-85823-73-8 Note: Související webová stránka: http://dx.doi.org/10.21136/panm.2022.20

Institution: Institute of Mathematics AS ČR
(web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences. Original record: https://hdl.handle.net/11104/0342395