Generalized Inverses: Algorithms and Applications

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Series: Mathematics Research Developments
BISAC: MAT019000; SCI040000
DOI: https://doi.org/10.52305/MJVE4994

Generalized Inverses: Algorithms and Applications demonstrates some of the latest hot topics on generalized inverse matrices and their applications. Each article has been carefully selected to present substantial research results. Topics discussed herein include recent advances in exploring of generalizations of the core inverse, particularly in composing appropriate outer inverses and the Moore-Penrose inverse such as OMP, MPO and MPOMP inverses; in analyzing of properties of the BT inverse and the BT-order; in perturbation estimations for the Drazin inverse; in using generalized inverses to solve systems of quaternion matrix equations and Sylvester-type tensor equations under t-product; in computing and approximating the matrix generalized inverses by hyperpower family of iterative methods of arbitrary convergence order; and in studying of the weighted pseudoinverse matrices with singular indefinite weights.

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Table of Contents

Preface

Chapter 1. A Survey of Composite Generalized Inverses
(Predrag Stanimirović, Dijana Mosić, and Yimin Wei – Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia, et al.)

Chapter 2. The BT Inverse
(David E. Ferreyra and Saroj B. Malik – Department of Mathematics, National University of Rio Cuarto, Rio Cuarto, Argentina, et al.)

Chapter 3. Perturbation Estimations for the Drazin Inverse
(Haifeng Ma – School of Mathematical Science, Harbin Normal University, Harbin, China)

Chapter 4. Cramer’s Rules for Systems of Quaternion Matrix Equations
(Ivan I. Kyrchei – Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine)

Chapter 5. Solutions to Some Sylvester-Type Tensor Equations Under T-Product
(Zhuo-Heng He and Wei-Lu Qin – Department of Mathematics, Shanghai University, Shanghai, P. R. China)

Chapter 6. Towards Higher Order Dynamical Systems
(Vasilios N. Katsikis, Predrag Stanimirović, Spyridon D. Mourtas, Shuai Li, and Xinwei Cao – Department of Economics, National and Kapodistrian University of Athens, Athens, Greece, et al.)

Chapter 7. Weighted Moore-Penrose Inverse with Indefinite Singular Weights
(Oleksandr M. Khimich, Ivan V. Sergienko, and Natalia A. Vareniuk – Department of Numerical Methods and Computer Modeling, V. M. Glushkov Institute of Cybernetics, NAS of Ukraine, Kyiv, Ukraine, et al.)

Index

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