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Generalizations of composite inverses with certain image and/or kernel

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  • 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
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    References listed on IDEAS

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    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. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. 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.
    4. 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.
    5. 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).
    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. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    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.
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