摘要：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 𝑋0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.
