Splines in Numerical Integration

AMS Subj. Classification: 65D07, 65D30.

We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the cardinal B-spline of arbitrary order and described five methods for calculation of the moments in the case when cardinal B-spline of order m,m ∈ N, is a weight function.