The Construction Of Some Optimal 2D Cubature Formulae

In this paper, we showcase some formulae that have been derived using the least squares optimisation method, which produces cubatures that are superior for use with singular integrals. We consider some formulae of standard and well-known structure for two differing weight functions, (i) w(x, y)=1 and (ii) w(x, y)= \sqrt{x^2 + y^2} .

Keywords:

• 2d Cubature Formulae
• Optimisation
• Maxwell's Formula
• Albrecht And Collatz Formula
• Radon's Formula