This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular value decomposition me...This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular value decomposition method. Some further results are also given to characterize the solution. Using these results, a numerical algorithm is introduced and some numerical results are provided to illustrate the effectiveness of the algorithm. Key words volume-preserving - procrustes problems - singular value decomposition MSC2000 65F30 - 65K10 Project supported by NNSFC (Grant No. 10371076), E-Institutes of Shanghai Municipal Education Commission (Grant No. N. E03004)展开更多
We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions： given matrices A ∈ R^n×n and B ∈ R^n×k, n 〉 k, minimize the residual ‖AQ- B‖F over the Stiefel manifold of ort...We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions： given matrices A ∈ R^n×n and B ∈ R^n×k, n 〉 k, minimize the residual ‖AQ- B‖F over the Stiefel manifold of orthonormal matrices. Theoretical analysis on necessary conditions and sufficient conditions for optimal solutions of the unbalanced Procrustes problem is given.展开更多
文摘This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular value decomposition method. Some further results are also given to characterize the solution. Using these results, a numerical algorithm is introduced and some numerical results are provided to illustrate the effectiveness of the algorithm. Key words volume-preserving - procrustes problems - singular value decomposition MSC2000 65F30 - 65K10 Project supported by NNSFC (Grant No. 10371076), E-Institutes of Shanghai Municipal Education Commission (Grant No. N. E03004)
文摘We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions： given matrices A ∈ R^n×n and B ∈ R^n×k, n 〉 k, minimize the residual ‖AQ- B‖F over the Stiefel manifold of orthonormal matrices. Theoretical analysis on necessary conditions and sufficient conditions for optimal solutions of the unbalanced Procrustes problem is given.
