Abstract
Many subclasses of H-matrices have already been investigated in application areas of linear algebra. One of them is \(\textrm{SDD}_1\) matrices given in Peña (Adv Comput Math 35:357–373, 2011). In this paper, a new subclass of H-matrices, i.e., generalized \(\textrm{SDD}_1\)(\(\textrm{GSDD}_1\)) matrices, is considered. The relationship between \(\textrm{GSDD}_1\) matrices and other subclasses of H-matrices is analyzed. Infinity norm bounds for the inverse of a \(\textrm{GSDD}_1\) matrix A are given, using a scaling matrix that transforms A into a strictly diagonally dominant matrix. The given scaling matrix is also utilized to obtain error bounds for the linear complementarity problems when the related matrices are \(\textrm{GSDD}_1\) matrices. Numerical examples show that the obtained results can improve other existing bounds.
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Acknowledgements
The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions, which improve the original manuscript. This work is partly supported by Natural Science Foundations of Fujian Province of China (2020J01926) and Research Project of Department of Education of Fujian (JAT210429), Natural Science Foundations of Hainan Province of China (121MS001).
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Communicated by Jinyun Yuan.
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Dai, PF., Li, J. & Zhao, S. Infinity norm bounds for the inverse for \(\textrm{GSDD}_1\) matrices using scaling matrices. Comp. Appl. Math. 42, 121 (2023). https://doi.org/10.1007/s40314-022-02165-x
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DOI: https://doi.org/10.1007/s40314-022-02165-x
Keywords
- Infinity norm bounds
- \(\textrm{GSDD}_1\) matrices
- \(\textrm{SDD}\) matrices
- Error bounds
- Linear complementarity problem