Application of reproducing kernel method to construction of cubature formulas for cube and simplex (Q1316743)

Using the method of reproducing kernel the author constructs the cubature formulae on: the triangle, the 3-dimensional simplex, the \(n\)-dimensional cube and the \(n\)-dimensional simplex. For example, the cubature formulae for the square are obtained, with the algebraic degree of exactness \(2k+1\) and the number of the nodes \(k^ 2+4\), \(k=5,7\).