Computing eigenvalues of quasi-rational Said–Ball–Vandermonde matrices

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-08-22 DOI:10.1007/s10444-024-10191-y

Xiaoxiao Ma, Yingqing Xiao

引用次数: 0

Abstract

This paper focuses on computing the eigenvalues of the generalized collocation matrix of the rational Said–Ball basis, also called as the quasi-rational Said–Ball–Vandermonde (q-RSBV) matrix, with high relative accuracy. To achieve this, we propose explicit expressions for the minors of the q-RSBV matrix and develop a high-precision algorithm to compute these parameters. Additionally, we present perturbation theory and error analysis to further analyze the accuracy of our approach. Finally, we provide some numerical examples to demonstrate the high relative accuracy of our algorithms.

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计算准有理 Said-Ball-Vandermonde 矩阵的特征值

本文的重点是以较高的相对精度计算有理 Said-Ball 基广义配位矩阵（也称为准有理 Said-Ball-Vandermonde (q-RSBV) 矩阵）的特征值。为此，我们提出了 q-RSBV 矩阵最小值的明确表达式，并开发了计算这些参数的高精度算法。此外，我们还提出了扰动理论和误差分析，以进一步分析我们方法的准确性。最后，我们提供了一些数值示例来证明我们算法的高相对精度。

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

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.