We consider Lagrange interpolation with Spherical Harmonics of data located at the equiangular Cubed Sphere nodes. An approach based on a suitable Echelon Form of the associated Vandermonde matrix is carried out. As an outcome, a particular subspace of Spherical Harmonics is defined. This subspace possesses a high-frequency truncation, reminiscent of the rhomboidal truncation. Numerical results show the interest of this approach in various contexts. In particular, several examples of resolution of the Poisson equation on the sphere are displayed.

中文翻译：

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使用球谐函数对立方球体进行插值

我们考虑使用位于等角立方球体节点的数据的球谐函数进行拉格朗日插值。执行基于相关 Vandermonde 矩阵的合适梯形图的方法。结果，定义了球谐函数的特定子空间。该子空间具有高频截断，让人联想到菱形截断。数值结果显示了这种方法在各种情况下的兴趣。特别是，显示了球体上泊松方程的几个解析示例。