Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also gi...

Full description

Bibliographic Details
Main Authors: Zhigang Jia, Meixiang Zhao, Minghui Wang, Sitao Ling
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/681605
id doaj-f6e25254b2e9480191408a6fb097ea5e
record_format Article
spelling doaj-f6e25254b2e9480191408a6fb097ea5e2020-11-25T00:45:17ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/681605681605Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix EquationZhigang Jia0Meixiang Zhao1Minghui Wang2Sitao Ling3School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, ChinaSchool of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, ChinaDepartment of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, ChinaCollege of Science, China University of Mining and Technology, Jiangsu 221116, ChinaThe solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.http://dx.doi.org/10.1155/2014/681605
collection DOAJ
language English
format Article
sources DOAJ
author Zhigang Jia
Meixiang Zhao
Minghui Wang
Sitao Ling
spellingShingle Zhigang Jia
Meixiang Zhao
Minghui Wang
Sitao Ling
Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation
Journal of Applied Mathematics
author_facet Zhigang Jia
Meixiang Zhao
Minghui Wang
Sitao Ling
author_sort Zhigang Jia
title Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation
title_short Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation
title_full Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation
title_fullStr Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation
title_full_unstemmed Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation
title_sort solvability theory and iteration method for one self-adjoint polynomial matrix equation
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.
url http://dx.doi.org/10.1155/2014/681605
work_keys_str_mv AT zhigangjia solvabilitytheoryanditerationmethodforoneselfadjointpolynomialmatrixequation
AT meixiangzhao solvabilitytheoryanditerationmethodforoneselfadjointpolynomialmatrixequation
AT minghuiwang solvabilitytheoryanditerationmethodforoneselfadjointpolynomialmatrixequation
AT sitaoling solvabilitytheoryanditerationmethodforoneselfadjointpolynomialmatrixequation
_version_ 1725271060823146496

Similar Items