Representations and computation of the BT inverse and its randomized algorithms

This text explores characterizations of the BT inverse and proposes several methods for calculating the BT inverse. One of the representations examines the invertibility of an appropriate bordered matrix whose lower right block coincides with the BT inverse. Considerations of the BT inverse in relat...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 515
Main Authors: Ma, Haifeng, Chen, Hongbo, Stanimirović, Predrag S.
Format: Journal Article
Language:English
Published: Elsevier Inc 15.04.2026
Subjects:
BT inverse
Generalized inverse
Hartwig and Spindelböck’s decomposition
Moore-Penrose inverse
Randomized algorithm
Singular value decomposition
BT inverse
Randomized algorithm
Generalized inverse
Moore-Penrose inverse
Hartwig and Spindelböck’s decomposition
Singular value decomposition
ISSN:0096-3003
Online Access:Get full text
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Summary:This text explores characterizations of the BT inverse and proposes several methods for calculating the BT inverse. One of the representations examines the invertibility of an appropriate bordered matrix whose lower right block coincides with the BT inverse. Considerations of the BT inverse in relation to the group inverse and the standard matrix inverse are discussed. It is verified that the BT inverse solution is the unique solution to a specific class of constrained singular linear equations. Utilizing Cramer’s rule, we derive elementnwise solution of such systems. We also develop iterative methods for calculating the BT inverse and provide a criterion for the convergence of these methods. Modifications of the successive matrix square algorithm and the Newton iterative method are explored. The Singular Value Decomposition (SVD) approach for calculating the matrix BT inverse is developed. Additionally, the corresponding adopted Randomized SVD (RSVD) algorithm offers enhanced performance, making it a strong choice for large-scale data practical applications.
ISSN:0096-3003
DOI:10.1016/j.amc.2025.129850