Full Length ArticlePolynomial interpolation on interlacingrectangular grids

In this paper we establish the unisolvence of any interlacing pair of rectangular grids of points with respect to a large class of associated polynomial spaces. This includes interpolation on Padua points and the schemes of Morrow and Patterson (1978), Xu (1996), and Erb et al. (2016). We use Newton polynomials and divided differences and an apparently new formula for determinants of certain divided difference matrices.