On Bernoulli’s Method

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-05-24 DOI:10.1137/22m1528501

Tamás Dózsa, Ferenc Schipp, Alexandros Soumelidis

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1259-1277, June 2024.
Abstract. We generalize Bernoulli’s classical method for finding poles of rational functions using the rational orthogonal Malmquist–Takenaka system. We show that our approach overcomes the limitations of previous methods, especially their dependence on the existence of a so-called dominant pole, while significantly simplifying the required calculations. A description of the identifiable poles is provided, as well as an iterative algorithm that can be applied to find every pole of a rational function. We discuss automatic parameter choice for the proposed algorithm and demonstrate its effectiveness through numerical examples.

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关于伯努利方法

SIAM 数值分析期刊》第 62 卷第 3 期第 1259-1277 页，2024 年 6 月。摘要。我们利用有理正交 Malmquist-Takenaka 系统概括了伯努利寻找有理函数极点的经典方法。我们的研究表明，我们的方法克服了以前方法的局限性，特别是它们对所谓的主导极点存在的依赖性，同时大大简化了所需的计算。我们对可识别极点进行了描述，并提供了一种可用于找到有理函数每个极点的迭代算法。我们讨论了拟议算法的自动参数选择，并通过数值示例证明了其有效性。

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.