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

Abstract EN

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.