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High-Order Iterative Methods for the DMP Inverse

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  • Xiaoji Liu
  • Naping Cai

Abstract

We investigate two iterative methods for computing the DMP inverse. The necessary and sufficient conditions for convergence of our schemes are considered and the error estimate is also derived. Numerical examples are given to test the accuracy and effectiveness of our methods.

Suggested Citation

  • Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    • Handle: RePEc:hin:jjmath:8175935
    DOI: 10.1155/2018/8175935
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    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. Kyrchei, Ivan, 2017. "Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 1-16.
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    Cited by:

    1. Mosić, Dijana & Stanimirović, Predrag S. & Katsikis, Vasilios N., 2021. "Weighted composite outer inverses," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. 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.
    3. 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).
    4. 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).
    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. 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).

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