Article ID Journal Published Year Pages File Type
4634905 Applied Mathematics and Computation 2008 11 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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