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

Abstract EN

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 Z~i can also be obtained by the least-norm least-squares solution of matrix equation ∑i=1tMiZ-iNi=F-, in which Z-i=Zi-Z~i, F-=F-∑i=1tMiZ~iNi.

The given numerical examples illustrate the efficiency of this algorithm.