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Infinity norm bounds for the inverse of generalized \({SDD_2}\) matrices with applications

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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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Data sharing not applicable to this article as no data were generated or analyzed during the current study.

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Acknowledgements

The authors are thankful to the anonymous referees for their valuable comments to improve the paper.

Funding

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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Correspondence to Feng Wang.

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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

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