发表机构
University of Pittsburgh（匹兹堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究过参数化多项式插值中Runge现象与双重下降的类比，探讨三种基下最小范数系数，结果主要针对等距和切比雪夫点。
AI 中文摘要
多项式插值中的Runge现象常被视为机器学习中双重下降现象的经典类比。本文探讨了三种常用多项式基下的过参数化多项式插值：单项式基、切比雪夫基和勒让德基，其系数在$\ell^2$-范数下最小（对于单项式基，也考虑$\ell^1$-范数下最小的系数）。我们主要针对等距和切比雪夫数据点展示结果，但许多结果与采样的具体形式无关。
英文摘要
The Runge phenomenon in polynomial interpolation is often considered a classical analogue of the double descent phenomenon in machine learning. In this note, we explore overparameterized polynomial interpolation in three popular polynomial bases: Monomial, Chebyshev and Legendre basis with coefficients that are minimal in the $\ell^2$-norm (and, for the monomial basis, also those minimal in the $\ell^1$-norm). We present our results primarily for equidistant and Chebyshev data points, but many results are independent of the exact form of sampling.
