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An efficient matrix iteration family for finding the generalized outer inverse

Author

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  • Kansal, Munish
  • Kumar, Sanjeev
  • Kaur, Manpreet

Abstract

This paper presents a new iterative family for computing the generalized outer inverse with a prescribed range and null space of a given complex matrix. It is proved that the proposed methods achieve at least ninth-order of convergence. In general, the improved formulation of scheme uses only seven matrix multiplications at each iteration, but for the specific parameters, it uses only five matrix multiplications. The theoretical discussion on computational efficiency index is presented. Further, numerical results obtained are compared with existing robust methods to verify the theoretical analysis and higher computational efficiency. Several numerical examples, including rectangular, rank-deficient, large sparse, and non-singular matrices from the matrix computation tool-box (mctoolbox) are included. Further, the performance of methods is measured on randomly generated singular matrices and boundary value problem. It is demonstrated that the presented scheme gives improved results than the existing Schulz-type iterative methods for calculating the generalized inverse.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003666
    DOI: 10.1016/j.amc.2022.127292
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    References listed on IDEAS

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    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. 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.
    3. Stanimirović, Predrag S. & Roy, Falguni & Gupta, Dharmendra K. & Srivastava, Shwetabh, 2020. "Computing the Moore-Penrose inverse using its error bounds," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    4. 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.

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