G-decompositions of matrices and quadratic doubly stochastic operators

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...

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Main Authors: Ganikhodzaev, Rasul, Mukhamedov, Farrukh, Saburov, Mansoor
Format: Conference or Workshop Item
Language:English
Published: 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/12726/
http://irep.iium.edu.my/12726/
http://irep.iium.edu.my/12726/1/isasm2011_2.pdf
id iium-12726
recordtype eprints
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 Conference or Workshop Item 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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodzaev, Rasul
Mukhamedov, Farrukh
Saburov, Mansoor
G-decompositions of matrices and quadratic doubly stochastic operators
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.
format Conference or Workshop Item
author Ganikhodzaev, Rasul
Mukhamedov, Farrukh
Saburov, Mansoor
author_facet Ganikhodzaev, Rasul
Mukhamedov, Farrukh
Saburov, Mansoor
author_sort Ganikhodzaev, Rasul
title G-decompositions of matrices and quadratic doubly stochastic operators
title_short 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_sort g-decompositions of matrices and quadratic doubly stochastic operators
publishDate 2011
url http://irep.iium.edu.my/12726/
http://irep.iium.edu.my/12726/
http://irep.iium.edu.my/12726/1/isasm2011_2.pdf
first_indexed 2023-09-18T20:21:53Z
last_indexed 2023-09-18T20:21:53Z
_version_ 1777408161687273472

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