The purpose of this paper is to develop the anti-Gauss cubature rule for approximating integrals defined on the square whose integrand function may have algebraic singularities at the boundaries. An application of such a rule to the numerical solution of second-kind Fredholm integral equations is also explored. The stability, convergence, and conditioning of the proposed Nystr\"om-type method are studied. The numerical solution of the resulting dense linear system is also investigated and several numerical tests are presented.

翻译：本文旨在开发适用于定义在正方形上、被积函数可能在边界处具有代数奇异性的积分的反高斯求积规则。同时，探讨了将该规则应用于第二类弗雷德霍姆积分方程数值解的方法。研究了所提出的奈斯特罗姆型方法的稳定性、收敛性和条件性，并探讨了由此产生的稠密线性系统的数值解，给出了若干数值测试结果。