Premium
Achieving accuracy and efficiency in spherical modelling of real data
Author(s) -
Cavoretto R.,
De Rossi A.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2906
Subject(s) - spherical harmonics , computation , mathematics , interpolation (computer graphics) , stability (learning theory) , partition (number theory) , partition of unity , locality , algorithm , mathematical optimization , computer science , mathematical analysis , artificial intelligence , linguistics , philosophy , physics , combinatorics , machine learning , finite element method , thermodynamics , motion (physics)
In this paper, a hybrid approximation method on the sphere is analysed. As interpolation scheme, we consider a partition of unity method, such as the modified spherical Shepard method, which uses zonal basis functions plus spherical harmonics as local approximants. The associated algorithm is efficiently implemented and works well also when the amount of data is very large, as it is based on an optimized searching procedure. Locality of the method guarantees stability in numerical computations, and numerical results show good accuracy. Moreover, we aimed to discuss preservation of such features when the method and the related algorithm are applied to experimental data. To achieve this purpose, we considered the Magnetic Field Satellite data. The goal was reached, as efficiency and accuracy are maintained on several sets of real data. Copyright © 2013 John Wiley & Sons, Ltd.