ADI iteration for Lyapunov equations: A tangential approach and adaptive shift selection

DOI10.1016/j.apnum.2016.06.006zbMath1348.65079arXiv1312.1142OpenAlexW2972401824MaRDI QIDQ311667

Mohammad Hasan, M. Dambrine

Publication date: 13 September 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.1142

zbMATH Keywords

large-scale systemsnumerical examplesalgebraic Lyapunov equationrational Krylov subspacesADI iterationalternating directions implicit iteration

Mathematics Subject Classification ID

Cites Work

• Adaptive rational Krylov subspaces for large-scale dynamical systems
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• Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
• Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations
• Computing real low-rank solutions of Sylvester equations by the factored ADI method
• The ADI iteration for Lyapunov equations implicitly performsH2pseudo-optimal model order reduction
• Adaptive Tangential Interpolation in Rational Krylov Subspaces for MIMO Dynamical Systems
• An improved numerical method for balanced truncation for symmetric second-order systems
• Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Low Rank Solution of Lyapunov Equations
• Approximation of Large-Scale Dynamical Systems

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