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

Anti-Gauss cubature rules with applications to Fredholm integral equations on the square