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Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications

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  • Ma, Haifeng
  • Gao, Xiaoshuang
  • Stanimirović, Predrag S.

Abstract

This paper is a study on main properties and characterizations of the DMP inverse. Also, corresponding representations and computational procedures are derived. Particularly, an upgrade of the bordering method to the case of the DMP inverse is considered as well as applications of the DMP inverse in solving singular linear systems. Also, the DMP inverse of an upper block triangular matrix and its sign pattern are investigated. Furthermore, several computational procedures aimed to approximating the DMP inverse are developed, implemented and tested. The main of them are the limit representation, a revised successive matrix squaring iterations and the Gradient Neural Network (GNN) dynamical system. Finally, some perturbation bounds and continuity of the DMP inverse are studied.

Suggested Citation

  • Ma, Haifeng & Gao, Xiaoshuang & Stanimirović, Predrag S., 2020. "Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s009630032030165x
    DOI: 10.1016/j.amc.2020.125196
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    References listed on IDEAS

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    1. Pan, V.Y. & Soleymani, F. & Zhao, L., 2018. "An efficient computation of generalized inverse of a matrix," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 89-101.
    2. Deng, Chunyuan & Yu, Anqi, 2015. "Relationships between DMP relation and some partial orders," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 41-53.
    3. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    4. Ma, Haifeng, 2018. "Optimal perturbation bounds for the core inverse," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 176-181.
    5. Ma, Haifeng & Stanimirović, Predrag S., 2019. "Characterizations, approximation and perturbations of the core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 404-417.
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    Cited by:

    1. Stanimirović, Predrag S. & Mosić, Dijana & Wei, Yimin, 2022. "Generalizations of composite inverses with certain image and/or kernel," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Mosić, Dijana & Zhang, Daochang & Stanimirović, Predrag S., 2024. "An extension of the MPD and MP weak group inverses," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    3. Mosić, Dijana & Stanimirović, Predrag S., 2021. "Representations for the weak group inverse," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    4. Mosić, Dijana & Stanimirović, Predrag S., 2022. "Expressions and properties of weak core inverse," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    5. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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