An efficient algorithm for the submatrix constraint of the matrix equation A 1 X 1 B 1+A 2 X 2 B 2+···+A l X l B l =C
An efficient algorithm for the submatrix constraint of the matrix equation A 1 X 1 B 1+A 2 X 2 B 2+···+A l X l B l =C
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DOI：
10.1080/00207160.2012.689291
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发表时间：
2012-08
影响因子：
1.8
通讯作者：
Zhuo-hua Peng;Zi-Jian Zhou
中科院分区：
文献类型：
--
作者：
Zhuo-hua Peng;Zi-Jian Zhou
矩阵A=(Aij)∈Rn×n是双对称的，如果a ij=aij=an+1−j，n+1−i对所有的1≤i，j≤n，本文给出了一个求‖A1X1B1+A2X2B2+···+A L X L B L−C‖的有效算法，其中‖·‖是Frobenius范数，具有一个指定的中心主子矩阵是双对称的.该算法产生合适的[X1，X2，…，X L]使得‖A 1 X 1 B 1+A 2 X 2 B 2+···+A L X L B L在没有舍入误差的情况下，在有限迭代步长内−C‖=min。数值实验结果表明，该算法具有较快的收敛速度。
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.