Stable integration rules with scattered integration points

A general method for near-best approximations to functionals on Rd, using scattered-data information, is applied for producing stable multidimensional integration rules. The rules are constructed to be exact for polynomials of degree ⩽m and, for a quasi-uniform distribution of the integration points, it is shown that the approximation order is O(hm+1) where h is an average distance between the data points.