Abstract
A new subclass of H-matrices named generalized \(SDD_2\) (for shortly, \(GSDD_2\)) matrices is introduced and some properties of \(GSDD_2\) matrices are presented. The relationship between \(GSDD_2\) matrices and other subclasses of H-matrices is studied. Moreover, the infinity norm bounds for the inverse of \(GSDD_2\) matrices are provided. Using the proposed infinity norm bounds, error bounds of the linear complementarity problems for \(GSDD_2\) matrices are given, which improve some existing results. Numerical examples are given to illustrate the validity of new results.
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Acknowledgements
The authors are thankful to the anonymous referees for their valuable comments to improve the paper.
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This research is supported by Guizhou Provincial Science and Technology Projects (20191161), the High-Level Innovative Talent Project of Guizhou Province (GCC2023027) and the Natural Science Research Project of Department of Education of Guizhou Province (QJJ2022015, QJJ2023012).
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QL: original draft writing. WR: review writing and editing. FW: conceptualization, supervision, and funding acquisition. All authors read and approved the final manuscript.
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Li, Q., Ran, W. & Wang, F. Infinity norm bounds for the inverse of generalized \({SDD_2}\) matrices with applications. Japan J. Indust. Appl. Math. 41, 1477–1500 (2024). https://doi.org/10.1007/s13160-024-00658-2
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DOI: https://doi.org/10.1007/s13160-024-00658-2
Keywords
- Generalized \(SDD_2\) matrices
- SDD matrices
- \(SDD_2\) matrices
- Error bounds
- Infinity norm bounds
- Linear complementarity problems