Journal ArticleDOI
A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equations
J. Saniuk,I. Rhodes +1 more
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In this article, a new proof for the inequality tr (XY) \leq \parallel X ∈ {2} \cdot tr Y under the condition that X may be any square matrix.Abstract:
A new proof is presented for the inequality, tr (XY) \leq \parallel X \parallel_{2} \cdot tr Y . This argument is valid under the condition that Y be real symmetric nonnegative definite; X may be any square matrix.read more
Citations
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Eigenvalue Inequalities for Matrix Product
Fuzhen Zhang,Qingling Zhang +1 more
TL;DR: A family of eigenvalue inequalities for the product of a Hermitian matrix and a positive-semidefinite matrix is presented and the theorem contains or extends some existing results on trace and eigenvalues.
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Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
TL;DR: An approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace through a trace minimization problem on the Stiefel manifold.
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Exact Stability Analysis of 2-D Systems Using LMIs
TL;DR: It turns out that, by employing the generalized S-procedure, one can derive smaller size of LMIs so that the computational burden can be reduced.
Journal ArticleDOI
A matrix inequality
TL;DR: In this paper, a new matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equations is presented, and the improvement of the obtained result over the previously reported results is shown.
Journal ArticleDOI
Random quantum batteries
Francesco Caravelli,Francesco Caravelli,Ghislaine Coulter-De Wit,Luis Pedro García-Pintos,Luis Pedro García-Pintos,Alioscia Hamma,Alioscia Hamma +6 more
TL;DR: In this article, the average work extracted is equal to the difference between the initial energy and the energy of the state at infinite temperature, times a quantum efficiency factor (1+Q/d^2), with d the dimension of the Hilbert space.
References
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Journal ArticleDOI
Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation
TL;DR: Lower and upper bounds on the trace of the positive semidefinite solution of the algebraic matrix Riccati and Lyapunov equation are derived and results in a tighter bound as compared to the Upper bound for the maximal eigenvalue.
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On norm bounds for algebraic Riccati and Lyapunov equations
Rajni V. Patel,M. Toda +1 more
TL;DR: New lower bounds on the spectral norms of the positive definite solutions to the continuos and discrete algebraic matrix Riccati and Lyapunov equations are derived.
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A note on eigenvalue bounds in algebraic Riccati equation
TL;DR: In this paper, an upper bound on the maximum eigenvalue of the solution matrix K of the algebraic Riccati equation is established, and several lower bounds are derived for some of the largest eigenvalues of K.
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Lower bounds on the solution of Lyapunov matrix and algebraic Riccati equations
TL;DR: In this article, lower bounds for all the eigenvalues of the solution matrix K of the Lyapunov matrix equation are established, and a special case of this result is a generalization of that presented in [1]-[3], where lower bounds are given.
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On the discrete Lyapunov matrix equation
TL;DR: In this article, bounds for the arithmetic and the geometric means of the characteristic roots of the positive semidefinite solution to the discrete Lyapunov matrix equation are derived, and some bounds for their arithmetic and geometric means are derived.