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G-decompositions of matrices and quadratic doubly stochastic operators

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.

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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.

Item Type: Conference or Workshop Item (Full Paper)
Additional Information: 5537/12726
Uncontrolled Keywords: G-decomposition; doubly stochastic quadratic operator; stochastic matrix; substochastic matrix.
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: Dr. Farrukh Mukhamedov
Date Deposited: 29 Dec 2011 15:40
Last Modified: 28 Dec 2012 15:04
URI: http://irep.iium.edu.my/id/eprint/12726

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