The study of interpolation nodes and their associated Lebesgue constants are central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow-Patterson points, a set of interpolation nodes introduced to construct cubature formulas of a minimum number of points in the square for a fixed degree $n$. We prove that their Lebesgue constant growth is ${\cal O}(n^2)$ as was conjectured based on numerical evidence about twenty years ago in the paper by Caliari, M., De Marchi, S., Vianello, M., {\it Bivariate polynomial interpolation on the square at new nodal sets}, Appl. Math. Comput. 165(2) (2005), 261--274.

翻译：插值节点及其相关Lebesgue常数的研究是数值分析的核心问题，直接影响多项式逼近的稳定性和精度。本文探讨Morrow-Patterson点——这是为在正方形区域上构造固定次数$n$下具有最少点数的求积公式而引入的一组插值节点。我们证明其Lebesgue常数的增长阶为${\cal O}(n^2)$，该结论验证了约二十年前Caliari, M., De Marchi, S., Vianello, M.在论文《Bivariate polynomial interpolation on the square at new nodal sets》（Appl. Math. Comput. 165(2) (2005), 261--274）中基于数值证据提出的猜想。