The Hermitian \(R\)-conjugate generalized Procrustes problem
type: Item
instance of: scholarly article
title: The Hermitian \(R\)-conjugate generalized Procrustes problem
zbMATH Open document ID: 1291.15035
DOI: 10.1155/2013/423605
author: Haixia Chang
author: Xuefeng Duan
author: Qing-Wen Wang
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We consider the Hermitian \(R\)-conjugate generalized Procrustes problem to find Hermitian \(R\)-conjugate matrix \(X\) such that \(\sum^p_{k=1}||A_kX-C_k||^2+\sum^q_{l=1}||XB_l-D_l||^2\) is minimum, where \(A_k\), \(C_k\), \(B_l\), and \(D_l(k=1,2,\dots,p,l=1,\dots,q)\) are given complex matrices, and \(p\) and \(q\) are positive integers. The expression of the solution to Hermitian \(R\)-conjugate generalized Procrustes problem is derived. And the optimal approximation solution in the solution set for Hermitian \(R\)-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 \(R\)-conjugate solution to the linear system of complex matrix equations \(A_1X=C_1\), \(A_2X=C_2,\dots,A_pX=C_p\), \(XB_1=D_1,\dots,XB_q=D_q\) (\(p\) and \(q\) 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.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 6306824
Wikidata QID: Q58916261
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/423605
OpenAlex ID: W1965298284
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description: scientific article; zbMATH DE number 6306824