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Abstract
Matrix A=(a
ij
)∈R
n×n
is said to be bisymmetric if a
ij
=a
ji
=a
n+1−j, n+1−i
for all 1≤i, j≤n. In this paper, an efficient algorithm is presented for minimizing ‖A
1
X
1
B
1+A
2
X
2
B
2+···+A
l
X
l
B
l
−C‖, where ‖·‖ is the Frobenius norm and is bisymmetric with a specified central principal submatrix
. The algorithm produces suitable [X
1, X
2, …, X
l
] such that ‖A
1
X
1
B
1+A
2
X
2
B
2+···+A
l
X
l
B
l
−C‖=min within finite iteration steps in the absence of roundoff errors. The results of given numerical experiments show that the algorithm has fast convergence rate.
Acknowledgements
We are very grateful to the referees for their valuable comments and suggestions. This project is supported by Equation(1) National Natural Science Foundation of China (11071062 and 60974048), Equation(2)
Natural Science Foundation of Hunan Province (10JJ3065), Equation(3)
Scientific Research Fund of Hunan Provincial Education Department of China (10A033) and Equation(4)
Scientific Research Fund of Hunan Science and Technology Department (2010FJ3166).