# zbMATH — the first resource for mathematics

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.
##### MSC:
 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)