Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)

Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)

The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbatio...

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Main Author: Jing Li
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/575964
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spelling doaj-6a70d31632454a8ea58e0b88b90a40d62020-11-25T00:01:23ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/575964575964Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)Jing Li0School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, ChinaThe nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.http://dx.doi.org/10.1155/2013/575964
collection DOAJ
language English
format Article
sources DOAJ
author Jing Li
spellingShingle Jing Li
Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)
Abstract and Applied Analysis
author_facet Jing Li
author_sort Jing Li
title Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)
title_short Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)
title_full Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)
title_fullStr Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)
title_full_unstemmed Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0)
title_sort solutions and improved perturbation analysis for the matrix equation x-a*x-pa=q   (p>0)
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.
url http://dx.doi.org/10.1155/2013/575964
work_keys_str_mv AT jingli solutionsandimprovedperturbationanalysisforthematrixequationxaxpaqp0
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