标题： 关于莫罗-帕特森点的勒贝格常数 显示英文标题

标题： On the Lebesgue constant of the Morrow-Patterson points

摘要： 插值节点及其相关的Lebesgue常数的研究是数值分析的核心，影响多项式逼近的稳定性和准确性。 在本文中，我们将探讨Morrow-Patterson点，这是一组用于在正方形中构造固定次数$n$的最少点数的求积公式的插值节点。 我们证明了它们的Lebesgue常数增长为${\cal O}(n^2)$，正如二十多年前Caliari, M., De Marchi, S., Vianello, M.,{\it 在新的节点集上在平方上的二元多项式插值}，Appl. Math. Comput. 165(2) (2005), 261--274中的论文所基于的数值证据所推测的。 显示英文摘要

摘要： 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.