On ADMMbased methods for solving the nearness symmetric solution of the system of matrix equations A1XB1 = C1 and A2XB2 = C2 
yuning wu,Mingli Zeng 
Keywords:Matrix nearness problem; Symmetric solution; ADMM; Iterative method; Matrix equations; Global convergence 
Abstract: 
Two new equivalent forms of the matrix nearness problem are developed. Some sufficient and necessary conditions for a symmetric matrix X* being a solution of the considered problem are presented. Based on the new equivalent forms of the above problem and the idea of the alternating direction method with multipliers (ADMM), we establish two new iterative methods to compute its solution, and analyze the global convergence of the proposed algorithms. Numerical results demonstrate the efficiency of our methods. The development here is an extension of the recent work of Peng, Fang, Xiao and Du [{ SpringerPlus}, 5:1005, 2016] on the nearness symmetric solution of the matrix equation AXB=C. 



