{"title":"改进解决具有 $$\\mathcal {M}$ - 张量的多线性系统的高斯-赛德尔迭代法","authors":"Malihe Nobakht-Kooshkghazi, Mehdi Najafi-Kalyani","doi":"10.1007/s13160-023-00637-z","DOIUrl":null,"url":null,"abstract":"<p>The main objective of this paper is to solve multi-linear systems with strong <span>\\( \\mathcal {M}\\)</span>-tensors using preconditioned methods based on tensor splitting. In this paper, we propose a new preconditioned Gauss–Seidel iterative method for solving multi-linear systems. The convergence and comparison theorems of the proposed method are discussed. Finally, some numerical experiments are given to confirm our theoretical analysis and demonstrate the efficiency of the proposed method.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Improving the Gauss–Seidel iterative method for solving multi-linear systems with $$\\\\mathcal {M}$$ -tensors\",\"authors\":\"Malihe Nobakht-Kooshkghazi, Mehdi Najafi-Kalyani\",\"doi\":\"10.1007/s13160-023-00637-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The main objective of this paper is to solve multi-linear systems with strong <span>\\\\( \\\\mathcal {M}\\\\)</span>-tensors using preconditioned methods based on tensor splitting. In this paper, we propose a new preconditioned Gauss–Seidel iterative method for solving multi-linear systems. The convergence and comparison theorems of the proposed method are discussed. Finally, some numerical experiments are given to confirm our theoretical analysis and demonstrate the efficiency of the proposed method.</p>\",\"PeriodicalId\":50264,\"journal\":{\"name\":\"Japan Journal of Industrial and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-12-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Japan Journal of Industrial and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13160-023-00637-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japan Journal of Industrial and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13160-023-00637-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Improving the Gauss–Seidel iterative method for solving multi-linear systems with $$\mathcal {M}$$ -tensors
The main objective of this paper is to solve multi-linear systems with strong \( \mathcal {M}\)-tensors using preconditioned methods based on tensor splitting. In this paper, we propose a new preconditioned Gauss–Seidel iterative method for solving multi-linear systems. The convergence and comparison theorems of the proposed method are discussed. Finally, some numerical experiments are given to confirm our theoretical analysis and demonstrate the efficiency of the proposed method.
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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