Iterative algorithms for solving a class of complex conjugate and transpose matrix equations 
 
Authors:  AiGuo Wu Lingling LvGuangRen Duan 
 
Institution:  ^{a} Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China ^{b} Institute of Electric Power, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, PR China ^{c} Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China 
 
Abstract:  This paper is concerned with iterative solutions to a class of complex matrix equations, which include some previously investigated matrix equations as special cases. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of matrix equations. A sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools. By using some properties of the real representation, a convergence condition that is easier to compute is also given in terms of original coefficient matrices. A numerical example is employed to illustrate the effectiveness of the proposed methods. 
 
Keywords:  Iterative algorithm Conjugate Transpose Complex matrix equations Real representation 2Norm 
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