In this work, a family of symmetric interpolation points are generated on the four-dimensional simplex (i.e. the pentatope). These points are optimized in order to minimize the Lebesgue constant. The process of generating these points closely follows that outlined by Warburton in "An explicit construction of interpolation nodes on the simplex," Journal of Engineering Mathematics, 2006. Here, Warburton generated optimal interpolation points on the triangle and tetrahedron by formulating explicit geometric warping and blending functions, and applying these functions to equidistant nodal distributions. The locations of the resulting points were Lebesgue-optimized. In our work, we extend this procedure to four dimensions, and construct interpolation points on the pentatope up to order ten. The Lebesgue constants of our nodal sets are calculated, and are shown to outperform those of equidistant nodal distributions.

翻译：本文在四维单纯形（即五胞体）上生成了一族对称插值点。这些点经过优化以最小化勒贝格常数。生成过程紧密遵循Warburton在《工程数学杂志》（2006年）"单纯形上插值节点的显式构造"一文中概述的方法。Warburton通过构建显式几何扭曲与混合函数，并将这些函数应用于等距节点分布，在三角形和四面体上生成了最优插值点。所得点的位置经过勒贝格优化。本工作将此过程扩展到四维，并构建了最高十阶的五胞体插值点。我们计算了节点集的勒贝格常数，结果表明其性能优于等距节点分布。