A Cubic Class of Iterative Procedures for Finding the Generalized Inverses

Munish Kansal, Manpreet Kaur, Litika Rani and Lorentz Jäntschi ()
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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

Mathematics, 2023, vol. 11, issue 13, 1-18

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.

Keywords: generalized inverse; convergence analysis; Moore–Penrose inverse; order of convergence; singular matrices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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