@Article{JCM-7-4,
author = {},
title = {The Algebraic Perturbation Method for Generalized Inverses},
journal = {Journal of Computational Mathematics},
year = {1989},
volume = {7},
number = {4},
pages = {327--333},
abstract = {<p style="text-align: justify;">Algebraic perturbation methods were first proposed for the solution of nonsingular linear systems by R. E. Lynch and T. J. Aird [2]. Since then, the algebraic perturbation methods for generalized inverses have been discussed by many scholars [3]-[6]. In [4], a singular square matrix was perturbed algebraically to obtain a nonsingular matrix, resulting in the algebraic perturbation method for the Moore-Penrose generalized inverse. In [5], some results on the relations between nonsingular perturbations and generalized inverses of $m\times n$ matrices were obtained, which generalized the results in [4]. For the Drazin generalized inverse, the author has derived an algebraic perturbation method in [6]. <br/>In this paper, we will discuss the algebraic perturbation method for generalized inverses with prescribed range and null space, which generalizes the results in [5] and [6]. <br/>We remark that the algebraic perturbation methods for generalized inverses are quite useful. The applications can be found in [5] and [8]. <br/>In this paper, we use the same terms and notations as in [1]. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1989-JCM-9482},
url = {https://global-sci.com/article/86115/the-algebraic-perturbation-method-for-generalized-inverses}
}