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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 (should also be assigned at least one other classification number from Section 41-XX)