TY - JOUR T1 - ADMM-Based Methods for Nearness Skew-Symmetric and Symmetric Solutions of Matrix Equation $AXB = C$ AU - Yu , Dongmei AU - Chen , Cairong AU - Han , Deren JO - East Asian Journal on Applied Mathematics VL - 4 SP - 698 EP - 716 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.100719.230320 UR - https://global-sci.org/intro/article_detail/eajam/17949.html KW - ADMM, matrix nearness problem, global convergence, preconditioning, iterative method. AB -

New equivalent forms of a matrix nearness problem are proposed and necessary and sufficient conditions for a skew-symmetric or symmetric matrix $X$ to be a solution of the problem are obtained. In order to find approximate solutions of the problem, we employ two ADMM-based iterative methods and prove their global convergence. Numerical simulations demonstrate the effectiveness of the methods developed.