IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v378y2020ics009630032030165x.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032030165X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125196?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mosić, Dijana & Stanimirović, Predrag S., 2021. "Representations for the weak group inverse," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    2. 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).
    3. Mosić, Dijana & Stanimirović, Predrag S., 2022. "Expressions and properties of weak core inverse," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    4. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    2. Mosić, Dijana & Stanimirović, Predrag S., 2021. "Representations for the weak group inverse," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    3. Khosro Sayevand & Ahmad Pourdarvish & José A. Tenreiro Machado & Raziye Erfanifar, 2021. "On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus," Mathematics, MDPI, vol. 9(19), pages 1-23, October.
    4. Mosić, Dijana & Stanimirović, Predrag S., 2022. "Expressions and properties of weak core inverse," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    5. 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).
    6. 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.
    7. Ma, Haifeng & Mosić, Dijana & Stanimirović, Predrag S., 2023. "Perturbation Bounds for the Group Inverse and its Oblique Projection," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    8. Kansal, Munish & Kumar, Sanjeev & Kaur, Manpreet, 2022. "An efficient matrix iteration family for finding the generalized outer inverse," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    9. Ma, Haifeng & Stanimirović, Predrag S. & Mosić, Dijana & Kyrchei, Ivan I., 2021. "Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    10. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    11. Cordero, Alicia & Soto-Quiros, Pablo & Torregrosa, Juan R., 2021. "A general class of arbitrary order iterative methods for computing generalized inverses," Applied Mathematics and Computation, Elsevier, vol. 409(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s009630032030165x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.