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A general class of arbitrary order iterative methods for computing generalized inverses

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  • Cordero, Alicia
  • Soto-Quiros, Pablo
  • Torregrosa, Juan R.

Abstract

A family of iterative schemes for approximating the inverse and generalized inverse of a complex matrix is designed, having arbitrary order of convergence p. For each p, a class of iterative schemes appears, for which we analyze those elements able to converge with very far initial estimations. This class generalizes many known iterative methods which are obtained for particular values of the parameters. The order of convergence is stated in each case, depending on the first non-zero parameter. For different examples, the accessibility of some schemes, that is, the set of initial estimations leading to convergence, is analyzed in order to select those with wider sets. This wideness is related with the value of the first non-zero value of the parameters defining the method. Later on, some numerical examples (academic and also from signal processing) are provided to confirm the theoretical results and to show the feasibility and effectiveness of the new methods.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004707
    DOI: 10.1016/j.amc.2021.126381
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    References listed on IDEAS

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    1. Cong-Trang Nguyen & Yao-Wen Tsai, 2017. "Finite-Time Output Feedback Controller Based on Observer for the Time-Varying Delayed Systems: A Moore-Penrose Inverse Approach," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-13, May.
    2. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    3. A. S. Al-Fhaid & S. Shateyi & M. Zaka Ullah & F. Soleymani, 2014. "A Matrix Iteration for Finding Drazin Inverse with Ninth-Order Convergence," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    4. M. Kafaei Razavi & A. Kerayechian & M. Gachpazan & S. Shateyi, 2014. "A New Iterative Method for Finding Approximate Inverses of Complex Matrices," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, September.
    5. Spiros Chountasis & Vasilios N. Katsikis & Dimitrios Pappas, 2009. "Applications of the Moore-Penrose Inverse in Digital Image Restoration," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-12, November.
    6. F. Soleymani, 2012. "A Rapid Numerical Algorithm to Compute Matrix Inversion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, September.
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    Cited by:

    1. 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.
    2. Chein-Shan Liu & Chung-Lun Kuo & Chih-Wen Chang, 2024. "Matrix Pencil Optimal Iterative Algorithms and Restarted Versions for Linear Matrix Equation and Pseudoinverse," Mathematics, MDPI, vol. 12(11), pages 1-31, June.

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