The Positive Definite Solution of the Nonlinear Matrix Equation Xs−A*X−tA=Q. (12th March 2018)

• Record Type: Journal Article
• Authors: Meng, Jie; Kim, Hyun-Min
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 4(2018)
• Page Start: 398
• Page End: 412
• Publication Date: 2018-03-12
• Subjects: Banach space -- fixed-point iteration -- Hermitian positive definite -- matrix equation -- perturbation bound; 15A24 -- 65F10 -- 65H10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1369108
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we consider a nonlinear matrix equation . The uniqueness of positive definite solution without any extra condition when s ≥ t is obtained. A fixed-point iteration with stepsize parameter for finding the positive definite solution is proposed. A condition number and some new perturbation bounds of the unique positive definite solution are derived. Finally, some numerical examples are given to show the efficiency of the proposed iterative method and perturbation bounds.