IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v428y2022ics0096300322002338.html
   My bibliography  Save this article

Generalizations of composite inverses with certain image and/or kernel

Author

Listed:
  • Stanimirović, Predrag S.
  • Mosić, Dijana
  • Wei, Yimin

Abstract

Expressions which include the Moore-Penrose (MP) inverse with various generalized inverses have been popular topic in numerical linear algebra. The most general case was the combination of the MP inverse with outer inverses AR(B),N(C)(2), known as the composite outer inverses. Starting from well-known and useful Urquhart representation of generalized inverses, in this research we consider Φ1-composite outer inverses which are based on the replacements of AR(B),N(C)(2) by the more general expressions Φ1:=B(CAB)(1)C. Algorithms for symbolic and numeric computation of Φ1-composite outer inverses are proposed and corresponding examples are developed. In addition, Φ2-composite outer inverses arising from the replacements of the term AR(B),N(C)(2) in composite outer inverses by the expressions Φ2:=B(CAB)(2)C∈A{2}, are investigated.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322002338
    DOI: 10.1016/j.amc.2022.127155
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322002338
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127155?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. Ferreyra, D.E. & Levis, F.E. & Thome, N., 2018. "Maximal classes of matrices determining generalized inverses," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 42-52.
    2. Ivan I. Kyrchei, 2019. "Determinantal Representations of the Core Inverse and Its Generalizations with Applications," Journal of Mathematics, Hindawi, vol. 2019, pages 1-13, October.
    3. Stanimirović, Predrag S. & Ćirić, Miroslav & Lastra, Alberto & Sendra, Juan Rafael & Sendra, Juana, 2021. "Representations and symbolic computation of generalized inverses over fields," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    4. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    5. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    6. Predrag S. Stanimirović & Miroslav Ćirić & Igor Stojanović & Dimitrios Gerontitis, 2017. "Conditions for Existence, Representations, and Computation of Matrix Generalized Inverses," Complexity, Hindawi, vol. 2017, pages 1-27, June.
    7. 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).
    8. 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)

    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. 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).
    2. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Mosić, Dijana & Stanimirović, Predrag S., 2022. "Expressions and properties of weak core inverse," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    4. Chan, Eunice Y.S. & Corless, Robert M. & González-Vega, Laureano & Sendra, J. Rafael & Sendra, Juana, 2022. "Inner Bohemian inverses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    5. Mosić, Dijana & Stanimirović, Predrag S., 2021. "Representations for the weak group inverse," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    6. 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).
    7. 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).
    8. Ashim Kumar & Dijana Mosić & Predrag S. Stanimirović & Gurjinder Singh & Lev A. Kazakovtsev, 2022. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    9. Dijana Mosić & Predrag S. Stanimirović & Spyridon D. Mourtas, 2023. "Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    10. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    11. 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).
    12. Dilan Ahmed & Mudhafar Hama & Karwan Hama Faraj Jwamer & Stanford Shateyi, 2019. "A Seventh-Order Scheme for Computing the Generalized Drazin Inverse," Mathematics, MDPI, vol. 7(7), pages 1-10, July.
    13. 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.
    14. Stanimirović, Predrag S. & Ćirić, Miroslav & Lastra, Alberto & Sendra, Juan Rafael & Sendra, Juana, 2021. "Representations and symbolic computation of generalized inverses over fields," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    15. Haifa Bin Jebreen, 2019. "Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme," Mathematics, MDPI, vol. 7(8), pages 1-11, August.
    16. Jin Zhong & Lin Lin, 2023. "Core-EP Monotonicity Characterizations for Property- n Matrices," Mathematics, MDPI, vol. 11(11), pages 1-11, May.
    17. 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:428:y:2022:i:c:s0096300322002338. 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.