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A Cubic Class of Iterative Procedures for Finding the Generalized Inverses

Author

Listed:
  • Munish Kansal

    (School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, India)

  • Manpreet Kaur

    (Department of Mathematics, Lovely Professional University, Phagwara 144411, India)

  • Litika Rani

    (School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, India)

  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, Muncii Blvd. No. 103-105, Cluj-Napoca 400641, Romania)

Abstract

This article considers the iterative approach for finding the Moore–Penrose inverse of a matrix. A convergence analysis is presented under certain conditions, demonstrating that the scheme attains third-order convergence. Moreover, theoretical discussions suggest that selecting a particular parameter could further improve the convergence order. The proposed scheme defines the special cases of third-order methods for β = 0 , 1 / 2 , and 1 / 4 . Various large sparse, ill-conditioned, and rectangular matrices obtained from real-life problems were included from the Matrix-Market Library to test the presented scheme. The scheme’s performance was measured on randomly generated complex and real matrices, to verify the theoretical results and demonstrate its superiority over the existing methods. Furthermore, a large number of distinct approaches derived using the proposed family were tested numerically, to determine the optimal parametric value, leading to a successful conclusion.

Suggested Citation

  • Munish Kansal & Manpreet Kaur & Litika Rani & Lorentz Jäntschi, 2023. "A Cubic Class of Iterative Procedures for Finding the Generalized Inverses," Mathematics, MDPI, vol. 11(13), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3031-:d:1189292
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    References listed on IDEAS

    as
    1. Lee, Miyoung & Kim, Daehwan, 2017. "On the use of the Moore–Penrose generalized inverse in the portfolio optimization problem," Finance Research Letters, Elsevier, vol. 22(C), pages 259-267.
    2. 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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