SIAM journal on numerical analysis vol:39 issue:4 pages:1132-1145
We consider the problem of numerical integration for multivariate functions with respect to a radial symmetric weight. We prove that suitable spherical product algorithms have the optimal rate of convergence n(-k/d) for C-k-functions. We also study classes of integrands with a singularity that are C-k outside the origin. Standard algorithms have a high cost for such functions because they require that the function is smooth everywhere. We construct suitably modified spherical product algorithms with an optimal rate of convergence n(-k/d) also in this case. In the compact case, we can use modi ed spherical product Gauss formulas with a nonalgebraic degree of precision.