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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (5): 889-904.doi: 10.3969/j.issn.1005-3085.2025.05.007cstr: 32411.14.cjem.CN61-1269/O1.2025.05.007

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广义Nekrasov矩阵的新判据

李  琦,   王诗云,   吕振华,   孙  旭   

  1. 沈阳航空航天大学理学院，沈阳 110136
  • 收稿日期:2022-12-08 接受日期:2023-05-22 出版日期:2025-10-15 发布日期:2025-12-15
  • 通讯作者: 王诗云 E-mail: wsy0902@163.com
  • 基金资助:
    国家自然科学基金 (11701390; 12171323)；辽宁省兴辽英才计划 (XLYC2002017)；辽宁省教育厅项目 (JYTMS20230281)；沈阳航空航天大学引进人才科研启动基金 (19YB53).

New Criteria for Generalized Nekrasov Matrices

LI Qi,  WANG Shiyun,  LV Zhenhua,  SUN Xu   

  1. School of Science, Shenyang Aerospace University, Shenyang 110136
  • Received:2022-12-08 Accepted:2023-05-22 Online:2025-10-15 Published:2025-12-15
  • Contact: S. Wang. E-mail address: wsy0902@163.com
  • Supported by:
    The National Natural Science Foundation of China (11701390; 12171323); the Revitalization Talents Program of Liaoning Province (XLYC2002017); the  Department of Education Program of Liaoning Province (JYTMS20230281);
    the Start-up Grant for New Faculty of Shenyang Aerospace University (19YB53).

摘要：

广义Nekrasov矩阵也称为非奇异$H$-矩阵，有广泛的应用背景。判别一个矩阵是否为广义Nekrasov矩阵是一个重要的研究课题，吸引了大批学者的目光。给出了两组广义Nekrasov矩阵的新判定条件，通过构造对角线元素小于或等于1的正对角矩阵，放缩了Nekrasov和的下三角部分，从而得到较好的判别条件，并改进了已有的若干结论。为了进一步说明所研究结果，设计了4个算例，分别说明了两个结论互不包含，且二者都比现有的某些条件弱。放缩Nekrasov和的下三角部分的研究方法为广义Nekrasov矩阵的判别提供了新的思路。

关键词: 广义Nekrasov矩阵, Nekrasov和, Nekrasov和的下三角部分, 非奇异$H$-矩阵, 判别条件

Abstract:

Generalized Nekrasov matrices, also known as nonsingular H-matrices, have a wide range of applications. Judging whether a matrix is a generalized Nekrasov matrix is an important research topic, which has attracted the attention of a large number of scholars. In this paper, two new criteria for generalized Nekrasov matrices are proposed. By constructing a positive diagonal matrix with diagonal elements less than or equal to 1, the lower triangle part of Nekrasov sum was reduced and then the new criteria improved several existing results. In order to further illustrate the results proposed in this paper, four numerical examples are designed in the last section. The numerical examples show that each of two new criteria can be better than the other one and both are weaker than some existing conditions. The method of reducing the lower triangle part of Nekrasov sum provides a new idea for the discrimination of generalized Nekrasov matrices.

Key words: generalized Nekrasov matrices, Nekrasov sum, lower triangle part of Nekrasov sum, nonsingular $H$-matrices, criteria

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