An iterative algorithm for the centrosymmetric solutions and optimal approximation of AXB+CXD=F
Dongjin Yuan · Journal of Yangzhou University · 2008
Applying the conjugate gradient method,an iterative algorithm is presented to solve the constrained matrix equation AXB+CXD=F over centrosymmetric matrix X and its optimal approximation.When the matrix equation is consistent,its centrosymmetric solution can be obtained within finite iterative steps in the absence of round off errors for any initial centrosymmetric matrix X1,and its leastnorm centrosymmetric solution can be derived by choosing a suitable initial iterative matrix.Furthermore,its optimal approximation to a given matrix X0 can be obtained by finding the least-norm centrosymmetric solution of a new matrix equation AB+CD=F.Some numerical examples verify the efficiency of the algorithm.