关于脊函数直线插值问题的说明

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-12 DOI:arxiv-2408.06443

Azer Akhmedov, Vugar Ismailov

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引用次数: 0

摘要

本文讨论了用具有固定方向的脊函数的线性组合对直线进行插值的问题。通过使用一些几何和/或线性方程组，我们构造性地证明了不可能用具有两个固定方向的脊函数总和对任意三条或更多直线上的任意数据进行插值。在有更多直线和更多方向的一般情况下，则简化为在这些直线的结合处存在某些集合的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A note on the problem of straight-line interpolation by ridge functions

In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of linear equations, we constructively prove that it is impossible to interpolate arbitrary data on any three or more straight lines by sums of ridge functions with two fixed directions. The general case with more straight lines and more directions is reduced to the problem of existence of certain sets in the union of these lines.

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arXiv - MATH - Classical Analysis and ODEs

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