Name
Abstract | ||
|---|---|---|
An p×q matrix A is said to be (M,N)-symmetric if MAN=(MAN)T for given M∈Rn×p,N∈Rq×n. In this paper, the following (M,N)-symmetric Procrustes problem is studied. Find the (M,N)-symmetric matrix A which minimizes the Frobenius norm of AX-B, where X and B are given rectangular matrices. We use Project Theorem, the singular-value decomposition and the generalized singular-value decomposition of matrices to analysis the problem and to derive a stable method for its solution. The related optimal approximation problem to a given matrix on the solution set is solved. Furthermore, the algorithm to compute the optimal approximate solution and the numerical experiment are given. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.amc.2007.08.094 | Applied Mathematics and Computation |
Keywords | Field | DocType |
(M,N)-symmetric matrix,Procrustes problem,Optimal approximation | Singular value decomposition,Mathematical optimization,Combinatorics,Matrix (mathematics),Q-matrix,Symmetric matrix,Matrix norm,Orthogonal Procrustes problem,Solution set,Numerical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
198 | 1 | 0096-3003 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||