A method is presented for forming polynomial interpolants on squares and cubes, which are more efficient in the so-called Euclidean degree than other commonly used methods with the same number of collocation points. These methods have several additional desirable properties. The interpolants can be formed and evaluated via the FFT and have a minimally growing Lebesgue constant. The associated points achieve Gauss-Lobatto order accuracy in integration, out-performing tensor product Gauss-Legendre integration for many $C_\infty$ functions. This method is related to prior work on total degree efficient collocation points by Yuan Xu et al. [arXiv:math/0604604] [arXiv:0808:0180]

翻译：本文提出一种在正方形和立方体上构建多项式插值的方法，该方法在相同配置点数量下，其欧几里得度效率优于其他常用方法。这些方法还具有若干其他理想特性：插值可通过快速傅里叶变换构建与求值，且具有最小增长的勒贝格常数。相关配置点在积分中达到高斯-洛巴托阶精度，对于许多$C_\infty$函数，其表现优于张量积高斯-勒让德积分。本方法与袁旭等人先前关于全次数高效配置点的研究[arXiv:math/0604604] [arXiv:0808:0180]相关。