eng
Spherical basis function approximation with particular trend functions
nusl-521970
Segeth, Karel
Programs and Algorithms of Numerical Mathematics /21./
Jablonec nad Nisou (CZ)
20220619
2023
spherical interpolation
spherical radial basis function
inverse multiquadric
https://hdl.handle.net/11104/0342395
http://www.nusl.cz/ntk/nusl-521970
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.
10 s.
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