Researches On Procrustes Problems

In this paper, we consider the unbalanced Procrustes problem with orthogonal constraint: given matrix A ∈ R(n×n) and B ∈ R(n×k), n > k, minimize the residual \\AQ — B\\f over the Steifel manifold of orthonormal matrices. The paper consists of four chapters.In the first chapter, we give some introductions of Procrustes problem.In the second chapter, we investigate properties of solution for Procrustes problem with orthonormal constraints. We present structures and properties of solution for balanced Procrustes problem;and we also analyze properties and conditions of solution for unbalanced Procrustes problem.In the third chapter, We present a successive projection method(SPM) for solving unbalanced Procrustes problem, which base upon projection method for solving problems LSQE and balanced Procrustes problems. And we also discuss computational issues and convergence of SPM.In the last chapter, we talk about numerical results for SPM.