TY - JOUR
T1 - On some cubature formulas on the sphere
AU - Prestin, Jürgen
AU - Roşca, Daniela
PY - 2006/9/1
Y1 - 2006/9/1
N2 - We construct interpolatory cubature rules on the two-dimensional sphere, using the fundamental system of points obtained by Laín Fernández [Polynomial Bases on the Sphere, Logos-Verlag, Berlin, 2003; Localized polynomial bases on the sphere, Electron. Trans. Numer. Anal. 19 (2005) 84-93]. The weights of the cubature rules are calculated explicitly. We also discuss the cases when this cubature leads to positive weights. Finally, we study the possibility to construct spherical designs and the degree of exactness.
AB - We construct interpolatory cubature rules on the two-dimensional sphere, using the fundamental system of points obtained by Laín Fernández [Polynomial Bases on the Sphere, Logos-Verlag, Berlin, 2003; Localized polynomial bases on the sphere, Electron. Trans. Numer. Anal. 19 (2005) 84-93]. The weights of the cubature rules are calculated explicitly. We also discuss the cases when this cubature leads to positive weights. Finally, we study the possibility to construct spherical designs and the degree of exactness.
UR - http://www.scopus.com/inward/record.url?scp=33748138853&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2006.02.001
DO - 10.1016/j.jat.2006.02.001
M3 - Journal articles
AN - SCOPUS:33748138853
SN - 0021-9045
VL - 142
SP - 1
EP - 19
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 1
ER -