A new iterative algorithm for solving a class of matrix nearness problem (Q408473)

Summary: 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 with the matrix equations \(AXB = E\), \(CXD = F\), which arises frequently in experimental design. If we choose the initial iterative matrix \(X_0 = 0\), the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.