Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2): 563-577.doi: 10.1007/s42967-024-00457-z

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Infinity Norm Bounds for the Inverse of SDD1-Type Matrices with Applications

Yuanjie Geng, Yuxue Zhu, Fude Zhang, Feng Wang   

  1. College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, Guizhou, China
  • 收稿日期:2024-04-11 修回日期:2024-07-29 出版日期:2026-04-07 发布日期:2026-04-07
  • 通讯作者: Feng Wang,E-mail:wangf991@163.com E-mail:wangf991@163.com
  • 基金资助:
    This research is supported by Guizhou Provincial Science and Technology Projects (20191161) of China, the High-Level Innovative Talent Project of Guizhou Province (GCC2023027) of China, the Natural Science Research Project of Department of Education of Guizhou Province (QJJ2022015, QJJ2023012) of China, and the Research Foundation of Guizhou Minzu University (GZMUZK[2023]YB10) of China.

Infinity Norm Bounds for the Inverse of SDD1-Type Matrices with Applications

Yuanjie Geng, Yuxue Zhu, Fude Zhang, Feng Wang   

  1. College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, Guizhou, China
  • Received:2024-04-11 Revised:2024-07-29 Online:2026-04-07 Published:2026-04-07
  • Contact: Feng Wang,E-mail:wangf991@163.com E-mail:wangf991@163.com
  • Supported by:
    This research is supported by Guizhou Provincial Science and Technology Projects (20191161) of China, the High-Level Innovative Talent Project of Guizhou Province (GCC2023027) of China, the Natural Science Research Project of Department of Education of Guizhou Province (QJJ2022015, QJJ2023012) of China, and the Research Foundation of Guizhou Minzu University (GZMUZK[2023]YB10) of China.

摘要: A new subclass of H-matrices named \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices is introduced. The relationships between \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices and other subclasses of H-matrices are studied. Moreover, the infinite norm bounds for the inverse of \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices are provided. As applications, error bounds of the linear complementarity problems (LCPs) for \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices and strictly diagonally dominant (\begin{document}$ \textrm{SDD} $\end{document}) matrices strictly diagonally dominant (are also presented, which improve some existing bounds. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

关键词: \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices, Strictly diagonally dominant (SDD) matrices, Infinity norm, Linear complementarity problems (LCPs), Error bounds

Abstract: A new subclass of H-matrices named \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices is introduced. The relationships between \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices and other subclasses of H-matrices are studied. Moreover, the infinite norm bounds for the inverse of \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices are provided. As applications, error bounds of the linear complementarity problems (LCPs) for \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices and strictly diagonally dominant (\begin{document}$ \textrm{SDD} $\end{document}) matrices strictly diagonally dominant (are also presented, which improve some existing bounds. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

Key words: \begin{document}$ \textrm{SDD}_1 $\end{document}-type matrices, Strictly diagonally dominant (SDD) matrices, Infinity norm, Linear complementarity problems (LCPs), Error bounds

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