Iterative solutions to the extended Sylvesterconjugate matrix equations 
 
Authors:  AiGuo Wu Xianlin Zeng WeiJun Wu 
 
Institution:  ^{a} Information and Control Research Center, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China ^{b} Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China ^{c} National Key Laboratory of Antennas and Microwave Technology, Xidian University, Xi’an 710071, PR China 
 
Abstract:  This paper is concerned with iterative solutions to a class of complex matrix equations. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of complex matrix equations. The range of the convergence factor is given to guarantee that the proposed algorithm is convergent for arbitrary initial matrix by applying a real representation of a complex matrix as a tool. By using some properties of the real representation, a sufficient convergence condition that is easier to compute is also given by original coefficient matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods. 
 
Keywords:  Iterative algorithm Extended Sylvesterconjugate matrix equation Real representation 2Norm Convergence 
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