On convergents infinite products and some generalized inverses of matrix sequences
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 th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25197/1/25197.pdf |
| _version_ | 1796970711121657856 |
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| author | Kilicman, Adem Al-Zhour, Zeyad |
| author_facet | Kilicman, Adem Al-Zhour, Zeyad |
| author_sort | Kilicman, Adem |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T08:02:07Z |
| format | Article |
| id | upm.eprints-25197 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:02:07Z |
| publishDate | 2011 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-251972017-10-20T02:59:37Z http://psasir.upm.edu.my/id/eprint/25197/ On convergents infinite products and some generalized inverses of matrix sequences Kilicman, Adem Al-Zhour, Zeyad 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. Hindawi Publishing Corporation 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25197/1/25197.pdf 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 https://www.hindawi.com/journals/aaa/2011/536935/abs/ 10.1155/2011/536935 |
| spellingShingle | Kilicman, Adem Al-Zhour, Zeyad On convergents infinite products and some generalized inverses of matrix sequences |
| title | On convergents infinite products and some generalized inverses of matrix sequences |
| title_full | On convergents infinite products and some generalized inverses of matrix sequences |
| title_fullStr | On convergents infinite products and some generalized inverses of matrix sequences |
| title_full_unstemmed | On convergents infinite products and some generalized inverses of matrix sequences |
| title_short | On convergents infinite products and some generalized inverses of matrix sequences |
| title_sort | on convergents infinite products and some generalized inverses of matrix sequences |
| url | http://psasir.upm.edu.my/id/eprint/25197/1/25197.pdf |
| work_keys_str_mv | AT kilicmanadem onconvergentsinfiniteproductsandsomegeneralizedinversesofmatrixsequences AT alzhourzeyad onconvergentsinfiniteproductsandsomegeneralizedinversesofmatrixsequences |