An Ulm-like algorithm for generalized inverse eigenvalue problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-09 DOI:10.1007/s11075-024-01845-5

Yusong Luo, Weiping Shen

引用次数: 0

Abstract

In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math. 367, 112485 2020) for the GIEP, we propose here an Ulm-like algorithm for the GIEP. Compared with other existing methods for the GIEP, the proposed algorithm avoids solving the (approximate) Jacobian equations and so it seems more stable. Assuming that the relative generalized Jacobian matrices at a solution are nonsingular, we prove the quadratic convergence property of the proposed algorithm. Incidentally, we extend the work of Luo et al. (J. Nonlinear Convex Anal. 24, 2309–2328 2023) for the inverse eigenvalue problem (for short, IEP) to the GIEP. Some numerical examples are provided and comparisons with other algorithms are made.

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广义逆特征值问题的类乌尔姆算法

本文研究广义逆特征值问题（简称 GIEP）的数值解法。受 Ulm 的一般非线性方程求解方法和 Aishima 的 GIEP 算法（《计算应用数学》，367, 112485 2020 年）的启发，我们在此提出一种类似 Ulm 的 GIEP 算法。与其他现有的 GIEP 方法相比，我们提出的算法避免了求解（近似）雅各布方程，因此显得更加稳定。假设求解时的相对广义雅各布矩阵为非奇异值，我们证明了所提算法的二次收敛特性。顺便提一下，我们将 Luo 等人（J. Nonlinear Convex Anal.本文提供了一些数值示例，并与其他算法进行了比较。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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