A radial basis function generated finite-differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of applied mathematics, mathematical physics and myriad other application areas. Previous approaches needed restrictive uniformity in the node set, which the algorithm presented here does not require. By using RBF-FD approach, the proposed algorithm computes quadrature weights for N arbitrarily scattered nodes in only \(O(N\,\log N)\) operations with high orders of accuracy.

中文翻译：

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球体积上的近似积分

描述了径向基函数生成的有限差分（RBF-FD）启发技术，用于在三个维度上评估球体积上的确定积分。在应用数学，数学物理学和许多其他应用领域的许多领域中，这种方法都是必需的。先前的方法需要节点集中的限制性均匀性，这里提出的算法不需要这种一致性。通过使用RBF-FD方法，该算法仅以\（O（N \，\ log N）\）个运算即可为N个任意分散的节点计算正交权重，具有较高的精度。