Journal of Computational Physics
Probability density evolution analysis of engineering structures via cubature points
Computational Mechanics
Constructing cubature formulae of degree 5 with few points
Journal of Computational and Applied Mathematics
High-degree cubature Kalman filter
Automatica (Journal of IFAC)
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Higher-dimensional Gaussian weighted integration is of interest in probabilistic simulations. Motivated by the need for variance calculations with functions being at least quadratic, the family of degree 5 formulae is considered. Using an existing formula for the integration over the surface of an n-sphere, an efficient, new formula for Gaussian weighted integration is obtained. Several other formulae that have appeared in the numerical integration literature are also given. The number of function evaluations required by the formulae is compared to a minimal bound result. The degree 5 formulae are applied to simple test problems and the relative errors are compared.