G-decompositions of matrices and quadratic doubly stochastic operators
G.D Birkhoff characterized the set of extreme doubly stochastic matrices. Namely his result states as follows: the set of extreme points of the set of doubly stochastic matrices coincides with the set of all permutations matrices. One can consider a generalization of Birkhoff's result for nonl...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English |
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2011
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| Online Access: | http://irep.iium.edu.my/12726/ http://irep.iium.edu.my/12726/1/isasm2011_2.pdf |
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| author | Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Ganikhodzaev, Rasul |
| building | IIUM Repository |
| collection | Online Access |
| description | G.D Birkhoff characterized the set of extreme doubly stochastic matrices. Namely his result states as follows: the set of extreme points of the set of doubly stochastic
matrices coincides with the set of all permutations matrices. One can consider a generalization of Birkhoff's result for nonlinear doubly stochastic operators. Among all
nonlinear operators, the simplest one is a quadratic operator. In this work we introduce a notion of G-decomposition of matrices which enables to study Birkhoff's problem for quadratic G-doubly stochastic operators. We find necessary and sufficient conditions for the matrices having G-decomposition in the class of stochastic and substochastic matrices. We study geometrical structures of the set of those matrices. Moreover, we investigate extreme points of the sets of matrices having G-decompositions. |
| first_indexed | 2025-11-14T14:46:30Z |
| format | Proceeding Paper |
| id | iium-12726 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:46:30Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-127262012-12-28T07:04:30Z http://irep.iium.edu.my/12726/ G-decompositions of matrices and quadratic doubly stochastic operators Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics G.D Birkhoff characterized the set of extreme doubly stochastic matrices. Namely his result states as follows: the set of extreme points of the set of doubly stochastic matrices coincides with the set of all permutations matrices. One can consider a generalization of Birkhoff's result for nonlinear doubly stochastic operators. Among all nonlinear operators, the simplest one is a quadratic operator. In this work we introduce a notion of G-decomposition of matrices which enables to study Birkhoff's problem for quadratic G-doubly stochastic operators. We find necessary and sufficient conditions for the matrices having G-decomposition in the class of stochastic and substochastic matrices. We study geometrical structures of the set of those matrices. Moreover, we investigate extreme points of the sets of matrices having G-decompositions. 2011-11 Proceeding Paper NonPeerReviewed application/pdf en http://irep.iium.edu.my/12726/1/isasm2011_2.pdf Ganikhodzaev, Rasul and Mukhamedov, Farrukh and Saburov, Mansoor (2011) G-decompositions of matrices and quadratic doubly stochastic operators. In: International Seminar on the Application of Science & Mathematics 2011, 1-3 November 2011, Kuala Lumpur. http://uhsb.uthm.edu.my/isasm2011/ISASM2011%20FULL%20PAPER.pdf |
| spellingShingle | QA Mathematics Ganikhodzaev, Rasul Mukhamedov, Farrukh Saburov, Mansoor G-decompositions of matrices and quadratic doubly stochastic operators |
| title | G-decompositions of matrices and quadratic doubly stochastic operators |
| title_full | G-decompositions of matrices and quadratic doubly stochastic operators |
| title_fullStr | G-decompositions of matrices and quadratic doubly stochastic operators |
| title_full_unstemmed | G-decompositions of matrices and quadratic doubly stochastic operators |
| title_short | G-decompositions of matrices and quadratic doubly stochastic operators |
| title_sort | g-decompositions of matrices and quadratic doubly stochastic operators |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/12726/ http://irep.iium.edu.my/12726/ http://irep.iium.edu.my/12726/1/isasm2011_2.pdf |