{"title":"A new preconditioned Gauss-Seidel method for solving $${\\mathcal {M}}$$ -tensor multi-linear system","authors":"Xuan-Le An, Xin-Mei Lv, Shu-Xin Miao","doi":"10.1007/s13160-024-00670-6","DOIUrl":null,"url":null,"abstract":"<p>By utilizing some elements of each row of the majorization matrix associated with the coefficient tensor, we propose a preconditioner, and present the corresponding preconditioned Gauss–Seidel method for solving <span>\\({\\mathcal {M}}\\)</span>-tensor multi-linear system. Theoretically, we give the convergence and comparison theorems of the proposed preconditioned Gauss–Seidel method. Numerically, we show the correctness of theoretical results and the efficiency of the proposed preconditioner by some examples.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"59 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japan Journal of Industrial and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13160-024-00670-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
By utilizing some elements of each row of the majorization matrix associated with the coefficient tensor, we propose a preconditioner, and present the corresponding preconditioned Gauss–Seidel method for solving \({\mathcal {M}}\)-tensor multi-linear system. Theoretically, we give the convergence and comparison theorems of the proposed preconditioned Gauss–Seidel method. Numerically, we show the correctness of theoretical results and the efficiency of the proposed preconditioner by some examples.
期刊介绍：
Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.
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