On Hermitian positive definite solutions of matrix equation \(X+A^{\ast} X^{-2} A=I\).

DOI10.1016/S0024-3795(03)00530-5zbMath1035.15017MaRDI QIDQ1410724

Yuhai Zhang

Publication date: 15 October 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

iterative methodmatrix equationpositive definite solution

Mathematics Subject Classification ID

Related Items (21)

The iterative method for solving nonlinear matrix equation \(X^{s} + A^{*}X^{-t}A = Q\) ⋮ Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Perturbation analysis of the matrix equation \(X-A^*X^{-p}A=Q\) ⋮ Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation ⋮ Positive fixed points for a class of nonlinear operators and applications ⋮ Positive definite solutions of the matrix equations ⋮ Fixed point iterative methods for solving the nonlinear matrix equation \(X-A^*X^{-n}A=I\) ⋮ Some properties of the nonlinear matrix equation \(X^s + A^* X^{-t} A = Q\) ⋮ Perturbation estimates for the nonlinear matrix equation \(X-A^*X^qA=Q\) (\(0<q<1\)). ⋮ On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ On positive definite solutions of the nonlinear matrix equations \(X \pm A^* X^q A = Q\) ⋮ Positive definite solutions of the nonlinear matrix equation \(X+A^*X^qA=Q\) (\(q>0\)). ⋮ Solutions and improved perturbation analysis for the matrix equation \(X-A^\ast X^{-p}A=Q(p>0)\) ⋮ Thompson metric method for solving a class of nonlinear matrix equation ⋮ Some investigation on Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ On the positive operator solutions to an operator equation \(X-A^\ast X^{-t}A=Q\) ⋮ On Hermitian positive definite solution of the matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q\) ⋮ Perturbation analysis of the nonlinear matrix equation \(X - \sum_{i = 1}^m A_i^* X^{p i} A_i = Q\) ⋮ Positive definite solution of a class of nonlinear matrix equation ⋮ Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation

Cites Work

• Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
• On matrix equations \(X\pm A^*X^{-2}A=I\)
• Unnamed Item
• Unnamed Item

This page was built for publication: On Hermitian positive definite solutions of matrix equation \(X+A^{\ast} X^{-2} A=I\).