Construction of fully symmetric cubature formulae of degree 4k − 3 for fully symmetric planar regions

摘要

A new method is described for the construction of cubature formulae of degree 4k − 3 for two-dimensional symmetric regions. This method is a generalisation of the T-method. Some formulae of degree 5, 9, 13 and 17 for the square, the circle and the entire plane are constructed.