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Finite iterative algorithms for a common solution to a group of complex matrix equations
Authors:Ai-Guo Wu  Lingling LvMing-Zhe Hou
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:An iterative algorithm is constructed to give a common solution to a group of complex matrix equations. By using the proposed algorithm, the existence of a common solution can be determined automatically. When a common solution exists for this group of matrix equations, it is proven by using a real inner product in complex matrix spaces as a tool that a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a more general case. A numerical example is given to illustrate the effectiveness of the proposed method.
Keywords:Finite iterative algorithm  Complex matrix equation  Inner product space  Orthogonality  Convergence property
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