Iterative solutions to coupled Sylvester-conjugate matrix equations

Authors:
Ai-Guo Wu;Gang Feng;Guang-Ren Duan;Wei-Jun Wu
Affiliations:
Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong and Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, P ...;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China;National Key Laboratory of Antennas and Microwave Technology, Xidian University, Xi'an, PR China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper is concerned with iterative solutions to the coupled Sylvester-conjugate matrix equation with a unique solution. By applying a hierarchical identification principle, an iterative algorithm is established to solve this class of complex matrix equations. With a real representation of a complex matrix as a tool, a sufficient condition is given to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. In addition, a sufficient convergence condition that is easier to compute is also given by the original coefficient matrices. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.