Geodesic
Localized polynomial bases on the sphere
Electronic transactions on numerical analysis, Tome 19 (2005), pp. 84-93.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The subject of many areas of investigation, such as meteorology or crystallography, is the reconstruction of a continuous signal on the -sphere from scattered data. A classical approximation method is $polynomial\textcent interpolation$. Let denote the space of polynomials of degree at most on the unit sphere . As it is $\sterling $############# §$\copyright \ddot $ well known, the so-called $spherical harmonics$ form an orthonormal basis of the space . Since these functions $\sterling $### exhibit a poor localization behavior, it is natural to ask for better localized bases. Given , "! 7§$8\ddot #\\%(' ) ) ) ' 0 \%4365 $$###$$21 we consider the spherical polynomials H $$###$$ G H $textcent$CQ2RTS $$###$$ 9 CBED F YA`abB(c UCVXW A@ @ H H #PI where denotes the Legendre polynomial of degree normalized according to the condition . In this Q SBPFdS W W @ paper, we present systems of points on that yield localized polynomial bases of the above form.$
Classification : 41A05, 65D05, 15A12
Keywords: fundamental systems, localization, matrix condition, reproducing kernel 
@article{ETNA_2005__19__a3,
     author = {La{\'\i}n Fern\'andez, Noem{\'\i}},
     title = {Localized polynomial bases on the sphere},
     journal = {Electronic transactions on numerical analysis},
     pages = {84--93},
     publisher = {mathdoc},
     volume = {19},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__19__a3/}
}
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%J Electronic transactions on numerical analysis
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Laín Fernández, Noemí. Localized polynomial bases on the sphere. Electronic transactions on numerical analysis, Tome 19 (2005), pp. 84-93. http://geodesic.mathdoc.fr/item/ETNA_2005__19__a3/