Developing the CGLS algorithm for the least squares solutions of the general coupled matrix equations

In the present paper, we consider the minimum norm solutions of the general least squares problem parallel to(Sigma(a)(j=1) A1(j)X(j)B(1j) Sigma(a)(j=1) A2(j)X(j)B(2j . . .) Sigma(a)(j=1) Ap(j)X(j)B(pj))- (C-1 C-2 . . . C-p)parallel to = min By developing the conjugate gradient least square (CGLS) method, we construct an efficient iterative method to solve this problem. The constructed iterative method can compute the solution group of the problem within a finite number of iterations in the absence of roundoff errors. Also it is shown that the method is stable and robust. Finally, by some numerical experiments, we demonstrate that the iterative method is effective and efficient. Copyright (c) 2013 John Wiley & Sons, Ltd.