On the existence of extremal positive definite solutions of the nonlinear matrix equation

DOI10.1016/j.mcm.2009.12.021zbMath1203.15011OpenAlexW2041253537MaRDI QIDQ604124

Sumit K. Garg

Publication date: 8 November 2010

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2009.12.021

zbMATH Keywords

algorithmsconvergenceiterationnumerical examplesnonlinear matrix equationpositive definite matrixextremal positive solution

Mathematics Subject Classification ID

Related Items (12)

On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + \sum_{i = 1}^m A_i^\ast X^{- t_i} A_i = Q\) ⋮ Investigation of the existence and uniqueness of extremal and positive definite solutions of nonlinear matrix equations ⋮ On the perturbation estimates of the maximal solution for the matrix equation \(X + A^T \sqrt{X^{- 1}} A = P\) ⋮ The Hermitian positive definite solution of the nonlinear matrix equation ⋮ Necessary and sufficient conditions for the existence of a positive definite solution for the matrix equation \(X + \sum^m_{i = 1} A^T_i X^{\delta_i} A_i = I\) ⋮ Solvability for a nonlinear matrix equation ⋮ Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations ⋮ Positive definite solutions of the nonlinear matrix equation \(X+A^*X^qA=Q\) (\(q>0\)). ⋮ Existence and uniqueness of the positive definite solution for the matrix equation \(X=Q+A^\ast(\hat{X}-C)^{-1}A\) ⋮ The investigation on two kinds of nonlinear matrix equations ⋮ ON THE MATRIX EQUATIONS Y \pm B^{T}e^{-Y}B=I ⋮ On the perturbation analysis of the maximal solution for the matrix equation \(X - \sum\limits_{i=1}^m A_i^\ast X^{-1} A_i + \sum\limits_{j=1}^n B_j^\ast X^{-1} B_j = I\)

Cites Work

• Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\)
• On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\)
• On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
• On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
• On the existence of extremal positive definite solutions of a kind of matrix equation
• The iterative method for solving nonlinear matrix equation \(X^{s} + A^{*}X^{-t}A = Q\)
• On the matrix equation \(X+A^{T} \root 2^m \of {X^{-1}}A+I\)
• On the existence of a positive definite solution of the matrix equation
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equationX+A^TX⁻²A=I

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