Geodesic
Quadrature over the sphere
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 104-118.

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

Summary: Consider integration over the unit sphere in , especially when the integrand has singular behaviour $\sterling $######## in a polar region. In an earlier paper [4], a numerical integration method was proposed that uses a transformation that leads to an integration problem over the unit sphere with an integrand that is much smoother in the polar regions of the sphere. The transformation uses a $grading parameter$ . The trapezoidal rule is applied to the spherical $$###$$ coordinates representation of the transformed problem. The method is simple to apply, and it was shown in [4] to have convergence or better for integer values of . In this paper, we extend those results to non-integral §$\copyright \ddot $###$$ values of . We also examine superconvergence that was observed when is an odd integer. The overall results $$### ###$$ agree with those of [11], although the latter is for a different, but related, class of transformations.$$
Classification : 65D32
Keywords: spherical integration, trapezoidal rule, Euler-MacLaurin expansion 
@article{ETNA_2005__20__a9,
     author = {Atkinson, Kendall and Sommariva, Alvise},
     title = {Quadrature over the sphere},
     journal = {Electronic transactions on numerical analysis},
     pages = {104--118},
     publisher = {mathdoc},
     volume = {20},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a9/}
}
TY  - JOUR
AU  - Atkinson, Kendall
AU  - Sommariva, Alvise
TI  - Quadrature over the sphere
JO  - Electronic transactions on numerical analysis
PY  - 2005
SP  - 104
EP  - 118
VL  - 20
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2005__20__a9/
LA  - en
ID  - ETNA_2005__20__a9
ER  - 
%0 Journal Article
%A Atkinson, Kendall
%A Sommariva, Alvise
%T Quadrature over the sphere
%J Electronic transactions on numerical analysis
%D 2005
%P 104-118
%V 20
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2005__20__a9/
%G en
%F ETNA_2005__20__a9
Atkinson, Kendall; Sommariva, Alvise. Quadrature over the sphere. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 104-118. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a9/