{"title":"关于$ B_1 $-矩阵的一些新结果","authors":"Yan Li, Yaqiang Wang","doi":"10.3934/era.2023244","DOIUrl":null,"url":null,"abstract":"The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"11 suppl_1 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some new results for $ B_1 $-matrices\",\"authors\":\"Yan Li, Yaqiang Wang\",\"doi\":\"10.3934/era.2023244\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.\",\"PeriodicalId\":48554,\"journal\":{\"name\":\"Electronic Research Archive\",\"volume\":\"11 suppl_1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Research Archive\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/era.2023244\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Archive","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/era.2023244","RegionNum":4,"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
摘要
$ B_1 $-矩阵是$ P $-矩阵的一个子类，是作为$ B $-矩阵的推广引入的。本文给出了$ B_1 $-矩阵的几个性质。然后，得到了$ B_1 $-矩阵逆的无穷范数上界。进一步给出了$ B_1 $-矩阵线性互补问题的误差界。最后，给出了一些数值算例来说明我们的结果。
The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.
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