An algorithm for computing positive definite solutions of the nonlinear matrix equationX + A*X−1A = I

DOI10.1080/00207160310001603316zbMath1049.65033OpenAlexW2124588683MaRDI QIDQ4467348

Salah M. El-Sayed

Publication date: 9 June 2004

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160310001603316

zbMATH Keywords

algorithmconvergencenumerical experimentsiteration methodnonlinear matrix equationdiscrete-time algebraic Riccati matrix equationminimal positive definite solution

Mathematics Subject Classification ID

Related Items (4)

Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ Bauer's spectral factorization method for low order multiwavelet filter design ⋮ Some properties of the nonlinear matrix equation \(X^s + A^* X^{-t} A = Q\) ⋮ A new inversion-free method for a rational matrix equation

Cites Work

• Unnamed Item
• Unnamed Item
• 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 \(X+A^*X^{-1}A=Q\)
• Some properties for the existence of a positive definite solution of matrix equation \(X+A^*X^{-2^m}A=I\)
• On the matrix equation \(X+A^ TX^{-1}A=I\)
• On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
• Iterative solution of two matrix equations
• A two-sided iterative method for computing positive definite solutions of a nonlinear matrix equation
• On the existence of a positive definite solution of the matrix equation
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• Two iteration processes for computing positive definite solutions of the equation \(X-A^*X^{-n}A=Q\)

This page was built for publication: An algorithm for computing positive definite solutions of the nonlinear matrix equationX + A*X⁻¹A = I