For a graph G=(V,E), finding set of disjoint edges that do not share any vertices is called matching problem, and the maximum fundamental problem in theory distributed algorithms. Although local algorithms for approximate have been widely studied, exact has much studied. In fact, no algorithm faster than trivial upper bound O(n^2) rounds known general instance. this paper, we propose randomized...

‎In this paper‎, ‎an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed‎. ‎The convergence analysis of the algorithm is investigated‎. ‎We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions‎. ‎Finally‎, ‎some numerical examples are given to demons...