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On convergents infinite products and some generalized inverses of matrix sequences


Citation

Kilicman, Adem and Al-Zhour, Zeyad (2011) On convergents infinite products and some generalized inverses of matrix sequences. Abstract and Applied Analysis, 2011. art. no. 536935. pp. 1-20. ISSN 1085-3375; ESSN: 1687-0409

Abstract

The definition of convergence of an infinite product of scalars is extended to the infinite usual and Kronecker products of matrices. The new definitions are less restricted invertibly convergence. Whereas the invertibly convergence is based on the invertible of matrices; in this study, we assume that matrices are not invertible. Some sufficient conditions for these kinds of convergence are studied. Further, some matrix sequences which are convergent to the Moore-Penrose inverses A + and outer inverses AT,S (2) as a general case are also studied. The results are derived here by considering the related well-known methods, namely, Euler-Knopp, Newton-Raphson, and Tikhonov methods. Finally, we provide some examples for computing both generalized inverses AT,S (2) and A + numerically for any arbitrary matrix Am,n of large dimension by using MATLAB and comparing the results between some of different methods.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1155/2011/536935
Publisher: Hindawi Publishing Corporation
Keywords: Infinite products; Generalized inverses
Depositing User: Nur Farahin Ramli
Date Deposited: 16 Jul 2013 00:43
Last Modified: 20 Oct 2017 02:59
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2011/536935
URI: http://psasir.upm.edu.my/id/eprint/25197
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