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...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/536935 |
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| author | Adem Kiliçman Zeyad Al-Zhour |
| author_facet | Adem Kiliçman Zeyad Al-Zhour |
| author_sort | Adem Kiliçman |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-82bc857893b141f0a77d42c5760f1b89 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-82bc857893b141f0a77d42c5760f1b892025-02-03T01:02:34ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/536935536935On Convergents Infinite Products and Some Generalized Inverses of Matrix SequencesAdem Kiliçman0Zeyad Al-Zhour1Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), Selangor, 43400 Serdang, MalaysiaDepartment of Basic Sciences and Humanities, College of Engineering, University of Dammam (UD), P. O. Box 1982, Dammam 31451, Saudi ArabiaThe 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.http://dx.doi.org/10.1155/2011/536935 |
| spellingShingle | Adem Kiliçman Zeyad Al-Zhour On Convergents Infinite Products and Some Generalized Inverses of Matrix Sequences Abstract and Applied Analysis |
| 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://dx.doi.org/10.1155/2011/536935 |
| work_keys_str_mv | AT ademkilicman onconvergentsinfiniteproductsandsomegeneralizedinversesofmatrixsequences AT zeyadalzhour onconvergentsinfiniteproductsandsomegeneralizedinversesofmatrixsequences |