SIAM Journal on Scientific Computing, Volume 42, Issue 6, Page A4046-A4062, January 2020.
A rule for constructing interpolation nodes for (n)th degree polynomials on the simplex is presented. These nodes are simple to define recursively from families of 1D node sets, such as the Lobatto--Gauss--Legendre (LGL) nodes. The resulting nodes have attractive properties: they are fully symmetric, they match the 1D family used in construction on the edges of the simplex, and the nodes constructed for the ((d-1))-simplex are the boundary traces of the nodes constructed for the (d)-simplex. When compared using the Lebesgue constant to other explicit rules for defining interpolation nodes, the nodes recursively constructed from LGL nodes are nearly as good as the warp & blend nodes of Warburton [J. Engrg. Math., 56 (2006), pp. 247--262] in 2D (which, though defined differently, are very similar) and in 3D are better than other known explicit rules by increasing margins for (n > 6). By that same measure, these recursively defined nodes are not as good as implicitly defined nodes found by optimizing the Lebesgue constant or related functions, but such optimal node sets have yet to be computed for the tetrahedron. A reference Python implementation has been distributed as the recursivenodes package, but the simplicity of the recursive construction makes them easy to implement.

中文翻译：

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简化的递归，无参数，明确定义的插值节点

SIAM科学计算杂志，第42卷，第6期，第A4046-A4062页，2020年1月。
提出了构造单纯形上第（n）次多项式插值节点的规则。这些节点很容易从一维节点集族（例如Lobatto-Gauss-Legendre（LGL）节点）中递归定义。生成的节点具有吸引人的属性：它们是完全对称的，它们与在单纯形边上用于构造的一维族匹配，并且为（（d-1））-simplex构造的节点是所构造节点的边界轨迹（d）-单数。当使用Lebesgue常数与其他用于定义插值节点的显式规则进行比较时，从LGL节点递归构造的节点几乎与Warburton的翘曲和混合节点一样好[J. gr Math。，56（2006），pp.247--262]中的二维（尽管定义不同，（非常相似），并且在3D模式下，通过增加（n> 6）的边距，比其他已知的显式规则要好。通过相同的方法，这些递归定义的节点不如通过优化Lebesgue常数或相关函数找到的隐式定义的节点好，但是尚未为四面体计算出这样的最佳节点集。参考Python实现已作为递归节点包分发了，但是递归构造的简单性使其易于实现。