On a relationship between the \(\operatorname{T}\)-congruence Sylvester equation and the Lyapunov equation

DOI10.1016/j.cam.2017.05.044zbMath1373.15023arXiv1511.01597OpenAlexW2964330793MaRDI QIDQ1675358

Yuto Miyatake, Tomohiro Sogabe, Shao-Liang Zhang, Masaya Oozawa

Publication date: 27 October 2017

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

Full work available at URL: https://arxiv.org/abs/1511.01597

zbMATH Keywords

Lyapunov equation\(\operatorname{T}\)-congruence Sylvester equationthe tensor product

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Multilinear algebra, tensor calculus (15A69)

Related Items (5)

Fast enclosure for the minimal nonnegative solution to the nonsymmetric T-Riccati equation ⋮ Lopsided DSS iteration method for solving complex Sylvester matrix equation ⋮ Fast verified computation for the solution of the T-congruence Sylvester equation ⋮ Relation between the T-congruence Sylvester equation and the generalized Sylvester equation ⋮ On a transformation of the ∗-congruence Sylvester equation for the least squares optimization

Uses Software

• mctoolbox

Cites Work

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• On the Kronecker products and their applications
• Implicit QR algorithms for palindromic and even eigenvalue problems
• The solution of the equation \(AX + X^{\star}B =0\)
• The polynomial solution to the Sylvester matrix equation
• Lyapunov matrix equations in system stability and control.
• Structured Condition Numbers for Invariant Subspaces
• Accuracy and Stability of Numerical Algorithms
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

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