About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 423605, 9 pages
http://dx.doi.org/10.1155/2013/423605
Research Article

The Hermitian -Conjugate Generalized Procrustes Problem

1Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China
2School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
3Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 10 May 2013; Accepted 14 August 2013

Academic Editor: Masoud Hajarian

Copyright © 2013 Hai-Xia Chang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the Hermitian -conjugate generalized Procrustes problem to find Hermitian -conjugate matrix such that is minimum, where , , , and ( , ) are given complex matrices, and and are positive integers. The expression of the solution to Hermitian -conjugate generalized Procrustes problem is derived. And the optimal approximation solution in the solution set for Hermitian -conjugate generalized Procrustes problem to a given matrix is also obtained. Furthermore, we establish necessary and sufficient conditions for the existence and the formula for Hermitian -conjugate solution to the linear system of complex matrix equations , , ( and are positive integers). The representation of the corresponding optimal approximation problem is presented. Finally, an algorithm for solving two problems above is proposed, and the numerical examples show its feasibility.