Polynomial Interpolation of Function Averages on Interval Segments

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-07-25 DOI:10.1137/23m1598271

Ludovico Bruni Bruno, Wolfgang Erb

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1759-1781, August 2024.
Abstract. Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise to new theoretical and practical aspects that distinguish this problem considerably from classical nodal interpolation. We will analyze fundamental mathematical properties of this problem as existence, uniqueness, and numerical conditioning of its solution. In a few selected scenarios, we will provide concrete conditions for unisolvence and explicit Lagrange-type basis systems for its representation. To study the numerical conditioning, we will provide respective concrete bounds for the Lebesgue constant.

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区间段上函数平均值的多项式内插法

SIAM 数值分析期刊》第 62 卷第 4 期第 1759-1781 页，2024 年 8 月。摘要。受微分形式多项式近似的启发，我们研究了多项式插值问题的分析和数值特性，该问题依赖于区间段上的函数平均值。段数据的使用带来了新的理论和实践方面的问题，使该问题与经典的节点插值问题大为不同。我们将分析该问题的基本数学特性，如其解的存在性、唯一性和数值条件。在一些选定的情况下，我们将提供不孤立的具体条件，并为其表示提供明确的拉格朗日型基础系统。为了研究数值条件，我们将分别提供 Lebesgue 常数的具体边界。

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

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.