{"title":"An algorithm for the spectral radius of weakly essentially irreducible nonnegative tensors","authors":"","doi":"10.1007/s10092-023-00561-1","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we first define the weakly essentially irreducible nonnegative tensors and unify the definitions of essentially positive tensors, weakly positive tensors and generalized weakly positive tensors. Then an algorithm to find the spectral radius of weakly essentially irreducible nonnegative tensors is given based on the implicit translational transformation, and the linear convergence condition of the algorithm is analyzed using the directed graph of the matrix, and finally the computational efficiency of the related algorithms is compared using numerical examples.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calcolo","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10092-023-00561-1","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we first define the weakly essentially irreducible nonnegative tensors and unify the definitions of essentially positive tensors, weakly positive tensors and generalized weakly positive tensors. Then an algorithm to find the spectral radius of weakly essentially irreducible nonnegative tensors is given based on the implicit translational transformation, and the linear convergence condition of the algorithm is analyzed using the directed graph of the matrix, and finally the computational efficiency of the related algorithms is compared using numerical examples.
期刊介绍：
Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation.
The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory.
Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.
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