A Structure Preserving FGMRES Method for Solving Large Lyapunov Equations

DOI10.1007/978-3-642-25100-9_15zbMath1246.78036OpenAlexW313722857MaRDI QIDQ2905415

Matthias Bollhöfer, André K. Eppler

Publication date: 27 August 2012

Published in: Mathematics in Industry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-25100-9_15

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical methods for differential-algebraic equations (65L80) Direct numerical methods for linear systems and matrix inversion (65F05) Preconditioners for iterative methods (65F08) Model reduction in optics and electromagnetic theory (78M34)

Related Items (5)

Low rank methods for a class of generalized Lyapunov equations and related issues ⋮ Computational Methods for Linear Matrix Equations ⋮ Model order reduction for linear and nonlinear systems: a system-theoretic perspective ⋮ A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations ⋮ Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey

Cites Work

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• Low-rank iterative methods for projected generalized Lyapunov equations
• Iterative solution of the Lyapunov matrix equation
• Positive real and bounded real balancing for model reduction of descriptor systems
• Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Low Rank Solution of Lyapunov Equations
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• Multilevel Preconditioners Constructed From Inverse-Based ILUs

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