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On best p-norm approximation of discrete data by polynomials
IMA Journal of Numerical Analysis ( IF 2.3 ) Pub Date : 2023-12-09 , DOI: 10.1093/imanum/drad086
Michael S Floater 1
Affiliation  

In this note, we derive a solution to the problem of finding a polynomial of degree at most $n$ that best approximates data at $n+2$ points in the $l_{p}$ norm. Analogous to a result of de la Vallée Poussin, one can express the solution as a convex combination of the Lagrange interpolants over subsets of $n+1$ points, and the error oscillates in sign.

中文翻译:

关于多项式离散数据的最佳 p 范数近似

在这篇文章中,我们导出了一个解决问题的方法,即找到一个次数最多为 $n$ 的多项式,该多项式最接近 $l_{p}$ 范数中 $n+2$ 点的数据。类似于 de la Vallée Poussin 的结果,可以将解表示为 $n+1$ 点子集上拉格朗日插值的凸组合,并且误差以符号形式振荡。
更新日期:2023-12-09
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