Gradient Based Iterative Solutions for Sylvester-Conjugate Matrix Equations
Received:May 04, 2016  Revised:November 23, 2016
Key Word: Sylvester-conjugate matrix equations   iterative solutions   convergence   relaxation parameter  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11071033).
Author NameAffiliation
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 Sylvester-conjugate 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:2095-2651.2017.03.013
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