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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

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Dashnic-Zusmanovich型矩阵的子直和

戴平凡,   潘  攀   

  1. 三明学院信息工程学院，福建 三明 365004
  • 出版日期:2022-12-15 发布日期:2022-12-15
  • 基金资助:
    国家自然科学基金 (11671318)；福建省自然科学基金 (2020J01926)；大学生创新训练项目 (201911311041).

Subdirect Sum of Dashnic-Zusmanovich Type Matrices

DAI Pingfan,   PAN Pan   

  1. School of Information Engineering, Sanming University, Sanming, Fujian 365004
  • Online:2022-12-15 Published:2022-12-15
  • Supported by:
    The National Natural Science Foundation of China (11671318); the Natural Science Foundations of Fujian Province (2020J01926); the College Students Innovation Training Program (201911311041).

PDF (PC)

105

摘要：

两个方阵的子直和在矩阵补全问题、域分解方法的重叠子域、有限元的整体刚度矩阵中有重要应用。针对Dashnic-Zusmanovich型矩阵，应用分类思想和不等式放缩技术，给出了判定Dashnic-Zusmanovich型矩阵的子直和仍然是该类矩阵的一些容易检测的充分条件。数值例子表明所给条件真实有效。

关键词: 子直和, Dashnic-Zusmanovich型矩阵, 严格对角占优

Abstract:

The subdirect sum of two square matrices has important applications in the matrix completion problem, the overlapping subdomains of domain decomposition methods, and the global stiffness matrices in finite elements. Applying classification ideas and inequality scaling techniques to the Dashnic-Zusmanovich type matrices, we derive some easily checkable sufficient conditions for determining that the subdirect sum of the Dashnic-Zusmanovich type matrices remains such class of matrices. Numerical examples show that the given conditions are true and valid.

Key words: subdirect sum, Dashnic-Zusmanovich type matrices, strictly diagonally dominant

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