On the Moore-Penrose pseudo-inversion of block symmetric matrices and its application in the graph theory

Pavlíková, Soňa; Ševčovič, Daniel

doi:10.1016/j.laa.2023.05.016

Cited by 4 publications

(1 citation statement)

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“…The endeavors of the researchers in this study are not limited to pure theoretical investigations of the generalized inverse but also aim to obtain the deepest knowledge of its characteristics and study its potentail for solving practical problems arising in diverse areas of research. For instance, some of its implementations are discovered for digital image processing [1], control theory [2], detection of neurons in cerebral cortex through a magnetic field [3], machine learning [4], graph theory [5], control theory [6], robotics research [7], and chemical balancing [8].…”

Section: Introductionmentioning

confidence: 99%

A Cubic Class of Iterative Procedures for Finding the Generalized Inverses

et al. 2023

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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.

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