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The \(\gamma \)-diagonally dominant degree of Schur complements and its applications

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Abstract

In this paper, we obtain a new estimate for the (product) \(\gamma \)-diagonally dominant degree of the Schur complement of matrices. As applications we discuss the localization of eigenvalues of the Schur complement and present several upper and lower bounds for the determinant of strictly \(\gamma \)-diagonally dominant matrices, which generalizes the corresponding results of Liu and Zhang (SIAM J. Matrix Anal. Appl. 27 (2005) 665-674).

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Acknowledgements

The authors thank Dr. Shiyun Wang and Mr. Qi Li for their good suggestions which improve the presentation of this manuscript.

Funding

The work was supported by Guangxi Provincial Natural Science Foundation of China (No. 2023GXNSFAA026514) and the National Nature Science Foundation of China (No. 12171323,12301591).

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Authors and Affiliations

  1. School of Science, Shenyang Aerospace University, Shenyang, 110136, Liaoning, People’s Republic of China

    Zhenhua Lyu

  2. School of Science, Guilin University of Aerospace Technology, Guilin, Guangxi, 541004, People’s Republic of China

    Lixin Zhou

  3. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, 030024, People’s Republic of China

    Junye Ma

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  1. Zhenhua Lyu
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  2. Lixin Zhou
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  3. Junye Ma
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Correspondence to Lixin Zhou.

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Lyu, Z., Zhou, L. & Ma, J. The \(\gamma \)-diagonally dominant degree of Schur complements and its applications. Comp. Appl. Math. 43, 342 (2024). https://doi.org/10.1007/s40314-024-02868-3

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  • DOI: https://doi.org/10.1007/s40314-024-02868-3

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