An alternative approach for solving the quadratic matrix equation \(C^\ast X^\ast A X C + C^\ast X^\ast B + B^\ast X C + D = 0\)

DOI10.1016/j.cam.2021.113909zbMath1479.15015OpenAlexW3208621489MaRDI QIDQ2059675

Hao Liu, Yongxin Yuan, Huiting Zhang, Lina Liu

Publication date: 14 December 2021

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

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113909

zbMATH Keywords

singular value decompositionspectral decompositionMoore-Penrose inversequadratic matrix equation

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Numerical methods for matrix equations (65F45)

Cites Work

• Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications
• On the solvability of a certain class of quadratic matrix equations
• Second order adjoint matrix equations
• State covariance assignment problem with measurement noise: A unified approach based on a symmetric matrix equation
• Solvability conditions for the matrix equation \(X^TDX+AX+X^TB+C=0\)
• Towards a Generalized Singular Value Decomposition
• Assigning controllability and observability Gramians in feedback control
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Solutions of a second-order conjugate matrix equation
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
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