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Abstract
In this paper, an iterative method is presented for finding the bisymmetric solutions of a pair of consistent matrix equations A 1 XB 1=C 1, A 2 XB 2=C 2, by which a bisymmetric solution can be obtained in finite iteration steps in the absence of round-off errors. Moreover, the solution with least Frobenius norm can be obtained by choosing a special kind of initial matrix. In the solution set of the matrix equations, the optimal approximation bisymmetric solution to a given matrix can also be derived by this iterative method. The efficiency of the proposed algorithm is shown by some numerical examples.
Acknowledgements
This research work is granted financial support from Shanghai Science and Technology Committee (No. 062112065) and Natural Science Foundation of Zhejiang Province (No. Y607136). And the authors wish to express their thanks to two referees for helpful suggestions and comments.