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Gradient based and least squares based iterative algorithms for matrix equations AXB+CX T D=F. (English) Zbl 1210.65097
A gradient based iterative algorithm and a least squares based iterative algorithm are developed and presented for the solution of the matrix equation AXB+CX T D=F. The hierarchical identification principle is applied to the matrix equation in order to decompose the system under consideration into two subsystems and to derive the iterative algorithms by extending the iterative methods for solving Ax=b and AXB=F. Further 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 is used to verify the proposed methods.
65F30Other matrix algorithms
65F10Iterative methods for linear systems
15A24Matrix equations and identities
[1]Ding, F.; Chen, T.: Gradient based iterative algorithms for solving a class of matrix equations, IEEE transactions on automatic control 50, No. 8, 1216-1221 (2005)
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