Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\).

DOI10.1016/S0024-3795(03)00424-5zbMath1039.15005MaRDI QIDQ1426295

Frank Uhlig, Ivan Ganchev Ivanov, Vejdi I. Hasanov

Publication date: 14 March 2004

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

perturbationnumerical experimentsRiccati equationpositive definite matrixmatrix equationperturbation estimate

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Miscellaneous inequalities involving matrices (15A45) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (14)

New upper and lower bounds, the iteration algorithm for the solution of the discrete algebraic Riccati equation ⋮ Solutions and perturbation estimates for the matrix equations \(X\pm A^*X^{-n}A=Q\) ⋮ Perturbation analysis of the matrix equation \(X-A^*X^{-p}A=Q\) ⋮ Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ On positive definite solutions of nonlinear matrix equation \(X^s-A^{*}X^{-t}A=Q\) ⋮ Nonrecursive solution for the discrete algebraic Riccati equation and \(X + \mathcal A^\ast X^{-1}\mathcal A=L\) ⋮ Perturbation analysis for solutions of \(X \pm A^{\ast}X^{-n} A = Q\) ⋮ Notes on two perturbation estimates of the extreme solutions to the equations \(X\pm A^{*}X^{-1}A=Q\) ⋮ Solutions and improved perturbation analysis for the matrix equation \(X-A^\ast X^{-p}A=Q(p>0)\) ⋮ An iterative method to solve a nonlinear matrix equation ⋮ Newton's iterative method to solve a nonlinear matrix equation ⋮ Perturbation analysis of the nonlinear matrix equation \(X - \sum_{i = 1}^m A_i^* X^{p i} A_i = Q\) ⋮ Notes on the Hermitian positive definite solutions of a matrix equation ⋮ On two perturbation estimates of the extreme solutions to the equations \(X \pm A^*X^{-1}A = Q\)

Cites Work

• On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
• Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
• Scaling of the discrete-time algebraic Riccati equation to enhance stability of the Schur solution method
• Perturbation Theory for Algebraic Riccati Equations
• Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)

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