Gradient Based Iterative Solutions for SylvesterConjugate Matrix Equations 
Received:May 04, 2016 Revised:November 23, 2016 
Key Word:
Sylvesterconjugate matrix equations iterative solutions convergence relaxation parameter

Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11071033). 
Author Name  Affiliation  Hailong SHEN  Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China  Cheng PENG  Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China  Xinhui SHAO  Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China  Tie ZHANG  Department of Mathematics, Northeastern University, Liaoning 110819, P. R. China 

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Abstract: 
This paper presents a gradient based iterative algorithm for Sylvesterconjugate matrix equations with a unique solution. By introducing a relaxation parameter and applying the hierarchical identification principle, an iterative algorithm is constructed to solve Sylvester matrix equations. By applying a real representation of a complex matrix as a tool and using some properties of the real representation, convergence analysis indicates that the iterative solutions converge to the exact solutions for any initial values under certain assumptions. Numerical examples are given to illustrate the efficiency of the proposed approach. 
Citation: 
DOI:10.3770/j.issn:20952651.2017.03.013 
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