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

Duanmei Zhou, Guoliang Chen, Guoxing Wu & Xiangyun Zhang

DOI: 10.4208/jcm.1210-m4082

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.

  • Copyright

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 $X^s + A^*F(X)A = Q$ 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 $X^s + A^*F(X)A = Q$ 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, Perturbation bound, 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 and Xiangyun Zhang. (2013). On the Nonlinear Matrix Equation $X^s + A^*F(X)A = Q$ with $S≥ 1$. Journal of Computational Mathematics. 31 (2). 209-220. doi:10.4208/jcm.1210-m4082
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