(Anti-)Hermitian generalized (anti-)Hamiltonian solution to a system of matrix equations
type: Item
instance of: scholarly article
title: (Anti-)Hermitian generalized (anti-)Hamiltonian solution to a system of matrix equations
zbMATH Open document ID: 1407.15019
DOI: 10.1155/2014/539215
author: Juan Yu
author: Qing-Wen Wang
author: Chang-Zhou Dong
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equations \(A X = B\), \(X C = D\) are derived, respectively. Secondly, the optimal approximation solution \(\min_{X \in K} \parallel \widehat{X} - X \parallel\) is obtained, where \(K\) is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of the above system and \(\widehat{X}\) is the given matrix. Thirdly, the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solution and the corresponding numerical examples are presented.
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 7016691
Wikidata QID: Q59068352
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/539215
OpenAlex ID: W1990387559
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description: scientific article; zbMATH DE number 7016691