An iterative algorithm for the generalized reflexive solution of the matrix equations AXB = E,CXD = F

An iterative algorithm is constructed to solve the linear matrix equation pair a x b = e,c x d = f over generalized reflexive matrix x. when the matrix equation pair a x b = e,c x d = f is consistent over generalized reflexive matrix x,for any generalized reflexive initial iterative matrix x 1,the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. the unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. furthermore,the optimal approximate solution of axb = e,cxd = f for a given generalized reflexive matrix x 0 can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair ax̃b,= ẽ,cx̃d = f̃ with ẽ = e - ax 0 b,f̃ = f - cx 0d. finally,several numerical examples are given to illustrate that our iterative algorithm is effective. copyright © 2012 deqin chen et al.