A note on computing the generalized inverse A T,S (2) of a matrix A
The generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remov...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202013169 |
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| _version_ | 1832560615754825728 |
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| author | Xiezhang Li Yimin Wei |
| author_facet | Xiezhang Li Yimin Wei |
| author_sort | Xiezhang Li |
| collection | DOAJ |
| description | The generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse
A T,S (2) has been recently developed with the condition
σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. Numerical examples are given to illustrate our results. |
| format | Article |
| id | doaj-art-ae48afea8c5046d0a5ec828d79f47602 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ae48afea8c5046d0a5ec828d79f476022025-02-03T01:27:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0131849750710.1155/S0161171202013169A note on computing the generalized inverse A T,S (2) of a matrix AXiezhang Li0Yimin Wei1Department of Mathematics and Computer Science, Georgia Southern University, Statesboro, GA 30460, USADepartment of Mathematics, Fudan University, Shanghai 200433, ChinaThe generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. Numerical examples are given to illustrate our results.http://dx.doi.org/10.1155/S0161171202013169 |
| spellingShingle | Xiezhang Li Yimin Wei A note on computing the generalized inverse A T,S (2) of a matrix A International Journal of Mathematics and Mathematical Sciences |
| title | A note on computing the generalized inverse A T,S (2) of a matrix A |
| title_full | A note on computing the generalized inverse A T,S (2) of a matrix A |
| title_fullStr | A note on computing the generalized inverse A T,S (2) of a matrix A |
| title_full_unstemmed | A note on computing the generalized inverse A T,S (2) of a matrix A |
| title_short | A note on computing the generalized inverse A T,S (2) of a matrix A |
| title_sort | note on computing the generalized inverse a t s 2 of a matrix a |
| url | http://dx.doi.org/10.1155/S0161171202013169 |
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