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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 ›› 2020, Vol. 37 ›› Issue (1): 75-88.doi: 10.3969/j.issn.1005-3085.2020.01.007

• • 上一篇    下一篇

一类非奇异$H$矩阵的新判据

刘长太1,2,  徐  静1,  徐辉军1   

  1. 1- 扬州工业职业技术学院基础部，扬州  225127
    2- 贵州民族大学理学院，贵阳  550025
  • 收稿日期:2017-09-03 接受日期:2018-01-24 出版日期:2020-02-15 发布日期:2020-04-15
  • 基金资助:
    国家自然科学基金(11361074)；贵州省科学基金([2015]2073)；贵州省教育厅自然科学基金([2015]420).

New Criteria for Nonsingular $H$-matrices

LIU Chang-tai1,2,  XU Jing1,  XU Hui-jun1   

  1. 1- Department of Basic, Yangzhou Polytechnic Institute, Yangzhou 225127
    2- College of Science, Guizhou Minzu University, Guiyang 550025
  • Received:2017-09-03 Accepted:2018-01-24 Online:2020-02-15 Published:2020-04-15
  • Supported by:
    The National Natural Science Foundation of China (11361074); the Science Foundation of Guizhou Province ([2015]2073); the National Natural Science Foundation of the Education Department of Guizhou Province ([2015]420).

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摘要： 非奇异 $H$ 矩阵的判别在经济数学和控制论等诸多领域是非常重要的．利用不等式的放缩技巧和构造精巧的正对角阵，得到了一组新的非奇异 $H$ 矩阵的充分条件，该条件简捷而实用且改进和推广了相应的结论，达到了非奇异 $H$ 矩阵判别范围扩大的目的．最后用数值算例验证了该充分条件的优越性．

关键词: 非奇异 $H$ 矩阵, 广义 Nekrasov 矩阵, 广义严格对角占优矩阵, 不可约, 非零元素链

Abstract: To determine a given matrix is a  nonsingular $H$-matrix or not plays an important role in mathematical economics, control theory, and so on. To get more nonsingular $H$-matrices easily, several practical sufficient conditions for nonsingular $H$-matrices  are  obtained by constructing exquisite positive diagonal matrices and applying some technical of inequalities. The corresponding results are improved and extended. Advantages of these results are illustrated by a numerical example.

Key words: nonsingular $H$-matrices, generalized Nekrasov matrices, strictly generalized diagonally dominant matrices, irreducibility, nonzero elements chain

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