Multivariate polynomial interpolation based on Radon projections

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-09-13 DOI:10.1007/s11075-024-01938-1

Nguyen Anh Ngoc, Nguyen Van Khiem, Tang Van Long, Phung Van Manh

引用次数: 0

Abstract

We study multivariate polynomial interpolation based on Radon projections corresponding to the intersection of hyperplanes and the coordinate axes of \(\mathbb {R}^n\). We give a characterization of these hyperplanes which determine an interpolation polynomial uniquely. We also establish conditions such that the interpolation projectors based on Radon projections converge to the Taylor projector.

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基于拉顿投影的多变量多项式插值法

我们基于超平面与 \mathbb {R}^n\ 的坐标轴交点对应的 Radon 投影研究多变量多项式插值。我们给出了这些超平面的特征，它们唯一地决定了插值多项式。我们还建立了基于 Radon 投影的插值投影收敛于泰勒投影的条件。

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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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.