2-DIMENSIONAL MINIMAL CUBATURE FORMULAS AND MATRIX EQUATIONS

For strictly positive, linear, and centrally symmetric functionals in two dimensions the existence of cubature formulas attaining the known lower bounds is equivalent to the solvability of certain matrix equati ons under some constraints. Any solution generates a real ideal the co mmon roots of which are the nodes of the cubature formula. These resul ts are applied to construct an infinite number of minimal positive cub ature formulas of an arbitrary degree of erectness for one special, bu t classical, integral.