{"title":"Convergence analysis of the largest and smallest H-eigenvalues for a class of tensor sequences","authors":"Zhaofeng Lan, Jianxun Liu, Xianzhen Jiang","doi":"10.1007/s12190-024-02096-2","DOIUrl":null,"url":null,"abstract":"<p>This paper considers the convergence analysis of the H-eigenvalues for a class of real symmetric and convergent tensor sequences. We first establish convergence results of some sequences of points. Then we study the behaviors of the H-eigenvalues and H-eigenvectors of the convergent tensor sequence. In particular, we obtain the convergence properties of the largest and smallest H-eigenvalues of the tensor sequence. Eventually, the corresponding numerical results are presented to verify our theoretical findings.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"16 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02096-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
This paper considers the convergence analysis of the H-eigenvalues for a class of real symmetric and convergent tensor sequences. We first establish convergence results of some sequences of points. Then we study the behaviors of the H-eigenvalues and H-eigenvectors of the convergent tensor sequence. In particular, we obtain the convergence properties of the largest and smallest H-eigenvalues of the tensor sequence. Eventually, the corresponding numerical results are presented to verify our theoretical findings.
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
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