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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.
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems