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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 697947, 11 pages
Research Article

An Iterative Method for the Least-Squares Problems of a General Matrix Equation Subjects to Submatrix Constraints

School of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741001, China

Received 26 July 2013; Accepted 22 October 2013

Academic Editor: Debasish Roy

Copyright © 2013 Li-fang Dai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation , where ( ) are to be determined centro-symmetric matrices with given central principal submatrices. For any initial iterative matrices, we show that the least-squares solution can be derived by this method within finite iteration steps in the absence of roundoff errors. Meanwhile, the unique optimal approximation solution pair for given matrices can also be obtained by the least-norm least-squares solution of matrix equation , in which . The given numerical examples illustrate the efficiency of this algorithm.