Constructing cubature formulae for spheres and balls
The purpose of this paper is to use the correspondence on the sphere [cf. \textit{Y. Xu}, SIAM J. Math. Anal. 29, No.~3, 779-793 (1998; Zbl 0907.33005)] on the sphere. Also, using this correspondence, a number of cubature formulae for the Chebyshev weight function on the ball \(B(2)\) follows from the formulae for the surface measure on the sphere \(S(2)\). The authors devote their main effort to the construction of cubature formulae with respect to the Chebyshev weight function on \(B(2)\). These formulae that are different from the ones obtained from the correspondence will lead to new cubature formulate for the Lebesgue measure on the sphere. Several numerical examples are given.
scientific article; zbMATH DE number 1398800
scientific article