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Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices

Author

Listed:
  • Wenlong Zeng

    (Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China)

  • Jianzhou Liu

    (Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China)

  • Hongmin Mo

    (College of Mathematics and Statistics, Jishou University, Jishou 416099, China)

Abstract

It is necessary to explore more accurate estimates of the infinity norm of the inverse of a matrix in both theoretical analysis and practical applications. This paper focuses on obtaining a tighter upper bound on the infinite norm of the inverse of Dashnic–Zusmanovich-type (DZT) matrices. The realization of this goal benefits from constructing the scaling matrix of DZT matrices and the diagonal dominant degrees of Schur complements of DZT matrices. The effectiveness and superiority of the obtained bounds are demonstrated through several numerical examples involving random variables. Moreover, a lower bound for the smallest singular value is given by using the proposed bound.

Suggested Citation

  • Wenlong Zeng & Jianzhou Liu & Hongmin Mo, 2023. "Schur Complement-Based Infinity Norm Bound for the Inverse of Dashnic-Zusmanovich Type Matrices," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2254-:d:1144658
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    References listed on IDEAS

    as
    1. Yating Li & Yaqiang Wang, 2022. "Schur Complement-Based Infinity Norm Bounds for the Inverse of GDSDD Matrices," Mathematics, MDPI, vol. 10(2), pages 1-29, January.
    2. Cvetković, Lj. & Erić, M. & Peña, J.M., 2015. "Eventually SDD matrices and eigenvalue localization," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 535-540.
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