Hermitian Polynomial Matrix Equations and Applications

DOI10.1007/16618_2023_50OpenAlexW4377077937MaRDI QIDQ6117607

Mei-Xiang Zhao, Linlin Zhao, Zhi-Gang Jia

Publication date: 19 February 2024

Published in: Matrix and Operator Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/16618_2023_50

zbMATH Keywords

iteration methodmaximal solutionpolynomial matrix equationHermitian definite positivemaximal-like solution

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Matrix equations and identities (15A24) Equations involving linear operators, with operator unknowns (47A62) Perturbations of nonlinear operators (47H14) Numerical methods for matrix equations (65F45)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solvability and sensitivity analysis of polynomial matrix equation \(X^s + A^TX^tA = Q\)
• Perturbation analysis and condition numbers of symmetric algebraic Riccati equations
• Operator inequalities associated with Hölder-McCarthy and Kantorovich inequalities
• On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
• Matrix Riccati equations in control and systems theory
• On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
• Condition numbers of algebraic Riccati equations in the Frobenius norm
• A structured condition number for self-adjoint polynomial matrix equations with applications in linear control
• A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations
• A step toward a unified treatment of continuous and discrete time control problems
• On the nonlinear matrix equation \(X^p = A + M^T (X \# B) M\)
• Solvability theory and iteration method for one self-adjoint polynomial matrix equation
• Perturbation theory and backward error for \(AX - XB = C\)
• Transformations between discrete-time and continuous-time algebraic Riccati equations
• Sensitivity analysis of the algebraic Riccati equations
• The positive definite solution of the nonlinear matrix equation \(X^p = A + M(B + X^{-1})^{-1} M^\ast\)
• Conditioning of the Stable, Discrete-Time Lyapunov Operator
• A Schur method for solving algebraic Riccati equations
• Perturbation Theory for Algebraic Riccati Equations
• Structure-Preserving Algorithms for Periodic Discrete-Time Algebraic Riccati Equations
• Note on Perturbation Theory for Algebraic Riccati Equations
• Invariant metrics, contractions and nonlinear matrix equations
• Matrix inequalities
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)

This page was built for publication: Hermitian Polynomial Matrix Equations and Applications