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TW 301
R. Cools and J.-C. Santos-Leon
Cubature formulas of a nonalgebraic degree of precision
Abstract
In this paper, we deal with the construction of cubature formulas that are exact for polynomials and also for polynomials multiplied by r, where r is the Euclidean distance to the origin. A general lower bound for the number of nodes for a specified degree of precision is given. This bound is improved for centrally symmetric integrals. A set of constraints (consistency conditions) is introduced for the construction of fully symmetric formulas. For one dimension and arbitrary degree, it is shown that the lower bound is sharp for centrally symmetric integrals. For higher dimensions, this is only illustrated for low degrees.
report.pdf / mailto: R. Cools