The Algebraic Perturbation Method for Generalized Inverses

The Algebraic Perturbation Method for Generalized Inverses

Year:    1989

Journal of Computational Mathematics, Vol. 7 (1989), Iss. 4 : pp. 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].  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1989-JCM-9482

Journal of Computational Mathematics, Vol. 7 (1989), Iss. 4 : pp. 327–333

Published online:    1989-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    7

Keywords: