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

作者：Peng, Zhuo Hua^*; Zhou, Zi Jian

来源：International Journal of Computer Mathematics, 2012, 89(12): 1641-1662.

DOI：10.1080/00207160.2012.689291

• algorithm
• matrix equation
• central principal submatrix
• bisymmetric matrix
• least-squares solution

Matrix A = (a(ij)) is an element of R-nxn 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 parallel to A(1)X(1)B(1) + A(2)X(2)B(2) + ... + A(l)X(l)B(l) - C parallel to, where parallel to.parallel to is the Frobenius norm and X-i is an element of R-nixni (i = 1, 2, ... , l) is bisymmetric with a specified central principal submatrix [x(ij)](r <= i,j <= ni-r). The algorithm produces suitable [X-1, X-2,..., X-l] such that parallel to A(1)X(1)B(1) + A(2)X(2)B(2) + ... + A(l)X(l)B(l) - C parallel to = 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.

• 出版日期2012
• 单位湖南大学