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

摘要

An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation∑i=1t‍MiZiNi=F, whereZi(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 matricesZ~ican also be obtained by the least-norm least-squares solution of matrix equation∑i=1t‍MiZ-iNi=F-, in whichZ-i=Zi-Z~i,  F-=F-∑i=1t‍MiZ~iNi. The given numerical examples illustrate the efficiency of this algorithm.