Noskov, M. V. Cubature weight formulae of highest algebraic accuracy. (English. Russian original) Zbl 0803.65023 Comput. Math. Math. Phys. 32, No. 12, 1819-1820 (1992); translation from Zh. Vychisl. Mat. Mat. Fiz. 32, No. 12, 1993-1995 (1992). Using some known results about cubature formulae for trigonometric polynomials the author presents a method for constructing cubature formulae with the weight \(w(x_ 1, \dots, x_ n) = \prod^ n_{i = 1} (1 - x_ i^ 2)^{-1/2}\), which integrate exactly all algebraic polynomials of degree \(m\). In case \(m=2\) and \(m=3\) the resulting cubature formulae are of highest algebraic degree of precision. Reviewer: B.D.Bojanov (Sofia) MSC: 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures 41A63 Multidimensional problems Keywords:cubature formulae; trigonometric polynomials; algebraic polynomials; highest algebraic degree of precision PDFBibTeX XMLCite \textit{M. V. Noskov}, Comput. Math. Math. Phys. 32, No. 12, 1 (1992; Zbl 0803.65023); translation from Zh. Vychisl. Mat. Mat. Fiz. 32, No. 12, 1993--1995 (1992)