[1] Mu Jianfei, Huang Jianguo,. Some studies on finding the nearest volume-preserving matrix [J]. Journal of Southeast University (English Edition), 2005, 21 (1): 119-122. [doi:10.3969/j.issn.1003-7985.2005.01.026]
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Some studies on finding the nearest volume-preserving matrix(
)
求解最近保体矩阵问题的若干研究
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 21
- Issue:
- 2005 1
- Page:
- 119-122
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2005-03-30
Info
- Title:
- Some studies on finding the nearest volume-preserving matrix
- 求解最近保体矩阵问题的若干研究
- Author(s):
- Mu Jianfei; Huang Jianguo
- Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
- PACS:
- O241.1
- DOI:
- 10.3969/j.issn.1003-7985.2005.01.026
- Abstract:
- Finding the nearest volume-preserving matrix for a given matrix is studied.A matrix equation is first obtained, which is a necessary condition for the solution to the problem.Then the equation is solved by the singular value decomposition method.Some additional results are also provided to further characterize the solution.Using these results, a numerical algorithm is introduced and a numerical test is given to illustrate the effectiveness of the algorithm.
- 研究了求解给定矩阵的最近保体矩阵问题.首先导出该问题解所必须满足的一个矩阵方程, 然后用奇异值分解方法求解该矩阵方程;并获得了该问题解的其他更进一步的刻画条件.利用这些结果建立了一个求解算法, 并通过数值算例说明了该算法的有效性.
References:
[1] Warner F W. Foundations of differentiable manifolds and Lie groups [M].Berlin:Springer, 1983.
[2] Andersson L E, Elfving T.A constrained procrustes problem [J]., SIAM J Matrix Anal Appl, 1997, 18:124-139.
[3] Arun K S.A unitarily constrained total least squares problem in signal processing [J].SIAM J Matrix Anal Appl, 1992, 13(3):729-745.
[4] Higham N J.Computing a nearest symmetric positive semidefinite matrix [J].Linear Algebra and Its Applications, 1988, 103:103-118.
[5] Higham N J.The symmetric procrustes problem [J]. BIT, 1988, 28(1):133-143.
[6] Umeyama S.Least-squares estimation of transformation parameters between two point patterns [J].IEEE Trans Pattern Anal Mach Intelligence, 1991, 13(4):376-380.
[7] Zietak K.On approximation problems with zero-trace matrices [J].Linear Algebra and Its Applications, 1996, 247:169-183.
[8] Arnold V I.Mathematical methods of classical mechanics [M].Berlin:Springer, 1978.
[9] Cyganski D, Orr J A.Applications of tensor theory to object recognition and orientation determination [J].IEEE Trans Pattern Anal Mach Intelligence, 1985, 7(6):663-673.
[10] Golub G H, van Loan C F.Matrix computations [M].Baltimore:The Johns Hopkins University Press, 1989.
Memo
- Memo:
- Biography: Mu Jianfei(1961—), male, associate professor, jfmu@sjtu.edu.cn.