An iterative method for the least-squares problems of a general matrix equation subjects to submatrix constraints

An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation i=1tmizini=f,where zi (i=1,2,.,t) 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 zi can also be obtained by the least-norm least-squares solution of matrix equation i=1tmiz-ini=f-,in which z-i=zi-zi,f-=f-i=1tmizini. the given numerical examples illustrate the efficiency of this algorithm. © 2013 li-fang dai et al.