A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces,we propose a new iterative algorithm to solve the matrix nearness problem associated withthe matrix equations A X B = E , C X D = F , which arises frequently in experimental design. Ifwe choose the initial iterative matrixX 0 = 0 , the least Frobenius norm solution of these matrixequations is obtained. Numerical examples show that the new algorithm is feasible and effective.