{"title":"Nekrasov矩阵的对角-舒尔补","authors":"Shiyun Wang, Qi Li, Xu Sun, Zhenhua Lyu","doi":"10.13001/ela.2023.7941","DOIUrl":null,"url":null,"abstract":"The Schur and diagonal-Schur complements are important tools in many fields. It was revealed that the diagonal-Schur complements of Nekrasov matrices with respect to the index set $\\{1\\}$ are Nekrasov matrices by Cvetkovic and Nedovic [Appl. Math. Comput., 208:225-230, 2009]. In this paper, we prove that the diagonal-Schur complements of Nekrasov matrices with respect to any index set are Nekrasov matrices. Similar results hold for $\\Sigma$-Nekrasov matrices. We also present some results on Nekrasov diagonally dominant degrees. Numerical examples are given to verify the correctness of the results.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":"8 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diagonal-Schur complements of Nekrasov matrices\",\"authors\":\"Shiyun Wang, Qi Li, Xu Sun, Zhenhua Lyu\",\"doi\":\"10.13001/ela.2023.7941\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Schur and diagonal-Schur complements are important tools in many fields. It was revealed that the diagonal-Schur complements of Nekrasov matrices with respect to the index set $\\\\{1\\\\}$ are Nekrasov matrices by Cvetkovic and Nedovic [Appl. Math. Comput., 208:225-230, 2009]. In this paper, we prove that the diagonal-Schur complements of Nekrasov matrices with respect to any index set are Nekrasov matrices. Similar results hold for $\\\\Sigma$-Nekrasov matrices. We also present some results on Nekrasov diagonally dominant degrees. Numerical examples are given to verify the correctness of the results.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2023.7941\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13001/ela.2023.7941","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
The Schur and diagonal-Schur complements are important tools in many fields. It was revealed that the diagonal-Schur complements of Nekrasov matrices with respect to the index set $\{1\}$ are Nekrasov matrices by Cvetkovic and Nedovic [Appl. Math. Comput., 208:225-230, 2009]. In this paper, we prove that the diagonal-Schur complements of Nekrasov matrices with respect to any index set are Nekrasov matrices. Similar results hold for $\Sigma$-Nekrasov matrices. We also present some results on Nekrasov diagonally dominant degrees. Numerical examples are given to verify the correctness of the results.
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