This paper is concerned with the numerical approximation of Fredholm integral equations of the second kind. A Nystrom method based on the anti-Gauss quadrature formula is developed and investigated in terms of stability and convergence in appropriate weighted spaces. The Nystrom interpolants corresponding to the Gauss and the anti-Gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation, under suitable assumptions which are easily verified for a particular weight function. Hence, an error estimate is available, and the accuracy of the solution can be improved by approximating it by an averaged Nystrom interpolant. The effectiveness of the proposed approach is illustrated through different numerical tests.

中文翻译：

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用高斯和反高斯求积法则求解第二类 Fredholm 积分方程

本文涉及第二类 Fredholm 积分方程的数值逼近。开发了一种基于反高斯求积公式的 Nystrom 方法，并研究了适当加权空间中的稳定性和收敛性。与高斯和反高斯求积规则相对应的 Nystrom 插值被证明为方程的解提供上界和下界，在适当的假设下很容易验证特定的权重函数。因此，可以使用误差估计，并且可以通过使用平均 Nystrom 插值对其进行近似来提高解的准确度。通过不同的数值测试说明了所提出方法的有效性。