Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation

Xing Tao Wang; Yuan Min Li

doi:10.1080/00207160802684442

Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation

Xing Tao Wang
, Yuan Min Li

Faculty of Computing

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X+A*X ^-α A=Q(0<α≤1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.

Original language	English
Pages (from-to)	2542-2551
Number of pages	10
Journal	International Journal of Computer Mathematics
Volume	87
Issue number	11
DOIs	https://doi.org/10.1080/00207160802684442
State	Published - Sep 2010

Keywords

iterative algorithm
necessary and sufficient condition
nonlinear matrix equation
positive definite solution

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10.1080/00207160802684442

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title = "Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation",

abstract = "Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X+A*X -α A=Q(0<α≤1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.",

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author = "Wang, \{Xing Tao\} and Li, \{Yuan Min\}",

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AU - Li, Yuan Min

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N2 - Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X+A*X -α A=Q(0<α≤1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.

AB - Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X+A*X -α A=Q(0<α≤1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.

KW - iterative algorithm

KW - necessary and sufficient condition

KW - nonlinear matrix equation

KW - positive definite solution

UR - https://www.scopus.com/pages/publications/77956498014

U2 - 10.1080/00207160802684442

DO - 10.1080/00207160802684442

M3 - 文章

AN - SCOPUS:77956498014

SN - 0020-7160

VL - 87

SP - 2542

EP - 2551

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 11

ER -

Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation

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Keywords

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