Necessary and sufficient conditions for the existence of a Hermitian positive definite solution of a type of nonlinear matrix equations

DOI10.1155/2009/672695zbMath1184.15013OpenAlexW2107064515WikidataQ58649431 ScholiaQ58649431MaRDI QIDQ1036420

Hongkui Li, Xueting Liu, Wen-Ling Zhao, Fu Yi Xu

Publication date: 13 November 2009

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/45878

zbMATH Keywords

nonlinear matrix equationHermitian positive definite solutions

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (2)

New upper and lower bounds, the iteration algorithm for the solution of the discrete algebraic Riccati equation ⋮ On the iterative method for the system of nonlinear matrix equations

Cites Work

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• A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\)
• A note on the fixed-point iteration for the matrix equations \(X \pm A^* X^{-1}A=I\)
• Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
• Some properties for the existence of a positive definite solution of matrix equation \(X+A^*X^{-2^m}A=I\)
• On positive definite solutions of the family of matrix equations \(X+A^*X^{-n}A=Q\).
• Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
• On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• On Direct Methods for Solving Poisson’s Equations
• On matrix equations \(X\pm A^*X^{-2}A=I\)

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