Some properties for the existence of a positive definite solution of matrix equation \(X+A^*X^{-2^m}A=I\)

DOI10.1016/S0096-3003(01)00019-4zbMath1031.15015OpenAlexW2002965757MaRDI QIDQ1855663

Salah M. El-Sayed, Mahmoud M. El-Alem

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(01)00019-4

zbMATH Keywords

matrix equationpositive definite solution

Mathematics Subject Classification ID

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

Related Items (12)

Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation ⋮ Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\) ⋮ On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Positive definite solutions of the nonlinear matrix equation \(X+A^*X^qA=Q\) (\(q>0\)). ⋮ A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\) ⋮ On equations that are equivalent to the nonlinear matrix equation \(X+A^{*}X ^{-\alpha}A=Q\) ⋮ Some investigation on Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ An iterative method to solve a nonlinear matrix equation ⋮ Newton's iterative method to solve a nonlinear matrix equation ⋮ An algorithm for computing positive definite solutions of the nonlinear matrix equationX + A*X⁻¹A = I ⋮ On positive definite solutions of the nonlinear matrix equation \(X+A^* X^{-n} A=I\) ⋮ Necessary and sufficient conditions for the existence of a Hermitian positive definite solution of a type of nonlinear matrix equations

Cites Work

• Positive solutions to \(X=A-BX^{-1}B^*\)
• Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
• On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Recursive Algorithms for Solving a Class of Nonlinear Matrix Equations with Applications to Certain Sensitivity Optimization Problems
• Unnamed Item
• Unnamed Item

This page was built for publication: Some properties for the existence of a positive definite solution of matrix equation \(X+A^*X^{-2^m}A=I\)