Volume 31, Issue 2
On the Nonlinear Matrix Equation Xs + A*F(X)A = Q with S≥ 1

Duanmei Zhou, Guoliang Chen, Guoxing Wu & Xiangyun Zhang

J. Comp. Math., 31 (2013), pp. 209-220.

Published online: 2013-04

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  • Abstract

This work is concerned with the nonlinear matrix equation X^s + A^*F(X)A= Q with s ≥ 1. Several sufficient and necessary conditions for the existence and  uniqueness of the Hermitian positive semidefinite solution are derived, and perturbation bounds are presented.

  • Keywords

Nonlinear matrix equations Perturbation bound Hermitian positive definite solution

  • AMS Subject Headings

15A24 47H10 47H14 47J05.

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COPYRIGHT: © Global Science Press

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@Article{JCM-31-209, author = {Duanmei Zhou, Guoliang Chen, Guoxing Wu and Xiangyun Zhang}, title = {On the Nonlinear Matrix Equation Xs + A*F(X)A = Q with S≥ 1}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {2}, pages = {209--220}, abstract = {

This work is concerned with the nonlinear matrix equation X^s + A^*F(X)A= Q with s ≥ 1. Several sufficient and necessary conditions for the existence and  uniqueness of the Hermitian positive semidefinite solution are derived, and perturbation bounds are presented.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1210-m4082}, url = {http://global-sci.org/intro/article_detail/jcm/9730.html} }
TY - JOUR T1 - On the Nonlinear Matrix Equation Xs + A*F(X)A = Q with S≥ 1 AU - Duanmei Zhou, Guoliang Chen, Guoxing Wu & Xiangyun Zhang JO - Journal of Computational Mathematics VL - 2 SP - 209 EP - 220 PY - 2013 DA - 2013/04 SN - 31 DO - http://doi.org/10.4208/jcm.1210-m4082 UR - https://global-sci.org/intro/article_detail/jcm/9730.html KW - Nonlinear matrix equations KW - Perturbation bound KW - Hermitian positive definite solution AB -

This work is concerned with the nonlinear matrix equation X^s + A^*F(X)A= Q with s ≥ 1. Several sufficient and necessary conditions for the existence and  uniqueness of the Hermitian positive semidefinite solution are derived, and perturbation bounds are presented.

Duanmei Zhou, Guoliang Chen, Guoxing Wu & Xiangyun Zhang. (1970). On the Nonlinear Matrix Equation Xs + A*F(X)A = Q with S≥ 1. Journal of Computational Mathematics. 31 (2). 209-220. doi:10.4208/jcm.1210-m4082
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