{"title":"Improvement of S-type localization sets of C-eigenvalues for piezoelectric-type tensors","authors":"Wenlong Zeng , Qing-Wen Wang","doi":"10.1016/j.aml.2024.109357","DOIUrl":null,"url":null,"abstract":"<div><div>The <span><math><mi>C</mi></math></span>-eigenvalues of piezoelectric-type tensors are crucial for understanding both the piezoelectric and converse piezoelectric effects. He et al. (2021) introduced an <span><math><mi>S</mi></math></span>-type inclusion set to locate all <span><math><mi>C</mi></math></span>-eigenvalues of such tensors. However, a straightforward counterexample demonstrates that this method can occasionally be inaccurate. In this paper, we propose an improved <span><math><mi>S</mi></math></span>-type localization sets for the <span><math><mi>C</mi></math></span>-eigenvalues of piezoelectric-type tensors. Additionally, we demonstrate that the proposed eigenvalue localization sets improve upon a recent result. Finally, numerical experiments are conducted to validate the effectiveness of our main results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109357"},"PeriodicalIF":2.9000,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089396592400377X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The -eigenvalues of piezoelectric-type tensors are crucial for understanding both the piezoelectric and converse piezoelectric effects. He et al. (2021) introduced an -type inclusion set to locate all -eigenvalues of such tensors. However, a straightforward counterexample demonstrates that this method can occasionally be inaccurate. In this paper, we propose an improved -type localization sets for the -eigenvalues of piezoelectric-type tensors. Additionally, we demonstrate that the proposed eigenvalue localization sets improve upon a recent result. Finally, numerical experiments are conducted to validate the effectiveness of our main results.
压电型张量的 C 特征值对于理解压电效应和反压电效应至关重要。He 等人（2021 年）引入了一种 S 型包含集来定位此类张量的所有 C 特征值。然而，一个直接的反例表明，这种方法偶尔会不准确。在本文中，我们为压电型张量的 C 特征值提出了一种改进的 S 型定位集。此外，我们还证明了所提出的特征值定位集改进了最近的一个结果。最后，我们通过数值实验验证了主要结果的有效性。
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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