Gradient based and least squares based iterative algorithms for matrix equations AXB + CXD = F |
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Authors: | Li Xie Huizhong Yang |
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Affiliation: | Control Science and Engineering Research Center, Jiangnan University, Wuxi 214122, PR China |
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Abstract: | This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + CXTD = F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax = b and AXB = F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems. |
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Keywords: | Iterative algorithm Gradient search Least squares Lyapunov matrix equations Sylvester matrix equations |
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