In this paper we improve the cubature rules discussed in Sommariva and Vianello (2021) for the computation of integrals by radial basis functions (RBFs). More precisely, we introduce in the context of meshless cubature a leave-one-out cross validation criterion for the optimization of the RBF shape parameter. This choice allows us to get highly reliable and accurate results for any kind of both infinity and finite regularity RBF. The efficacy of this approximation scheme is tested by numerical experiments on complicated polygonal regions. The related Matlab software is provided to the scientific community in [1].

中文翻译：

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RBFCUB：通用多边形上近乎最优的无网格体积的数值包

在本文中，我们改进了 Sommariva 和 Vianello (2021) 中讨论的体积规则，用于通过径向基函数 (RBF) 计算积分。更准确地说，我们在无网格空间的背景下引入了一个留一法交叉验证标准，用于优化 RBF 形状参数。这种选择使我们能够为任何类型的无穷大和有限规律 RBF 获得高度可靠和准确的结果。这种近似方案的有效性通过复杂多边形区域的数值实验进行了测试。相关的Matlab软件在 [1] 中提供给科学界。