Iterative positive definite solutions of the two nonlinear matrix equations \(X \pm A^{T}X^{-2} A =I \)

DOI10.1016/j.amc.2004.04.080zbMath1072.65065OpenAlexW2048827285MaRDI QIDQ1774852

Naglaa M. El-Shazly, Mohamed A. Ramadan, Talaat S. El Danaf

Publication date: 4 May 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2004.04.080

zbMATH Keywords

iteration schemes

Mathematics Subject Classification ID

Related Items (10)

Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ On the nonlinear matrix equation \(X+A*X - qA=Q\) \((q\geq 1)\) ⋮ An efficient method for special least squares solution of the complex matrix equation \((AXB,CXD)=(E,F)\) ⋮ Iterative solutions to coupled Sylvester-transpose matrix equations ⋮ On positive definite solutions of nonlinear matrix equation \(X^s-A^{*}X^{-t}A=Q\) ⋮ An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices ⋮ On the matrix equation \(X+A^{T} \root 2^m \of {X^{-1}}A+I\) ⋮ On equations that are equivalent to the nonlinear matrix equation \(X+A^{*}X ^{-\alpha}A=Q\) ⋮ An iterative method to solve a nonlinear matrix equation ⋮ Newton's iterative method to solve a nonlinear matrix equation

Cites Work

• Ladder networks, fixpoints, and the geometric mean
• Functional calculus for sesquilinear forms and the purification map
• On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
• Stabilizability of Linear Systems Over a Commutative Normed Algebra with Applications to Spatially-Distributed and Parameter-Dependent Systems
• On Direct Methods for Solving Poisson’s Equations
• On matrix equations \(X\pm A^*X^{-2}A=I\)
• Unnamed Item

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