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Volume 7, Issue 4
The Algebraic Perturbation Method for Generalized Inverses

Jun Ji

J. Comp. Math., 7 (1989), pp. 327-333.

Published online: 1989-07

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  • Abstract

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].
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].
We remark that the algebraic perturbation methods for generalized inverses are quite useful. The applications can be found in [5] and [8].
In this paper, we use the same terms and notations as in [1].  

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@Article{JCM-7-327, author = {Jun Ji}, title = {The Algebraic Perturbation Method for Generalized Inverses}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {4}, pages = {327--333}, abstract = {

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].
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].
We remark that the algebraic perturbation methods for generalized inverses are quite useful. The applications can be found in [5] and [8].
In this paper, we use the same terms and notations as in [1].  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9482.html} }
TY - JOUR T1 - The Algebraic Perturbation Method for Generalized Inverses AU - Jun Ji JO - Journal of Computational Mathematics VL - 4 SP - 327 EP - 333 PY - 1989 DA - 1989/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9482.html KW - AB -

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].
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].
We remark that the algebraic perturbation methods for generalized inverses are quite useful. The applications can be found in [5] and [8].
In this paper, we use the same terms and notations as in [1].  

Jun Ji. (1989). The Algebraic Perturbation Method for Generalized Inverses. Journal of Computational Mathematics. 7 (4). 327-333. doi:
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