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On the Lyapunov and Stein equations

✍ Scribed by Fernando C. Silva; Rita Simões

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
155 KB
Volume
420
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let L ∈ C n×n and let H, K ∈ C n×n be Hermitian matrices. The general inertia theorem gives a complete set of relations between the similarity class of L and the congruence class of H, when the Lyapunov equation LH + HL * = K is satisfied and K > 0.

In this paper, we give some relations between the similarity class of L and the congruence class of K, when the Lyapunov equation is satisfied and H > 0.

We also consider the corresponding problem with the Stein equation.

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Specialized Parallel Algorithms for Solv
Specialized Parallel Algorithms for Solving Lyapunov and Stein Equations
✍ Enrique S. Quintana-Ortı́; Robert van de Geijn 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 215 KB

Lyapunov and Stein matrix equations arise in many important analysis and synthesis applications in control theory. The traditional approach to solving these equations relies on the QR algorithm which is notoriously difficult to parallelize. We investigate iterative solvers based on the matrix sign f