The iterative method for solving nonlinear matrix equation X s + A ∗ X − t A = Q

Nonlinear matrix equation X s + A ∗ X − t A = Q, where Q is an Hermitian positive definite matrix, A ∗ is the conjugate transpose of the matrix A and both of s and t are positive integers, has widely applied background. In this paper, necessary conditions and sufficient conditions for the existence...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 188; no. 1; pp. 46 - 53
Main Author Yueting, Yang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2007
Subjects
Hermitian positive definite solutions
Maximal solution
Nonlinear matrix equation
Perturbation bound
Hermitian positive definite solutions
Nonlinear matrix equation
Perturbation bound
Maximal solution
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Summary:Nonlinear matrix equation X s + A ∗ X − t A = Q, where Q is an Hermitian positive definite matrix, A ∗ is the conjugate transpose of the matrix A and both of s and t are positive integers, has widely applied background. In this paper, necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions of this equation are derived. An iterative method for obtaining Hermitian positive definite solutions is proposed. Moreover, a perturbation bound for the Hermitian positive definite solutions is given.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.09.085