On optimality of approximate low rank solutions of large-scale matrix equations

DOI10.1016/j.sysconle.2014.02.005zbMath1292.65040OpenAlexW2085361143WikidataQ115224018 ScholiaQ115224018MaRDI QIDQ2454151

Tobias Breiten, Peter Benner

Publication date: 13 June 2014

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2014.02.005

zbMATH Keywords

Lyapunov equationSylvester equationrational Krylov subspacesiterative rational Krylov algorithmlow rank approximations\(\mathcal H_2\)-model reductionlarge-scale matrix equationsRiemannian optimization method

Mathematics Subject Classification ID

Related Items (8)

Model order reduction for linear and nonlinear systems: a system-theoretic perspective ⋮ Computing real low-rank solutions of Sylvester equations by the factored ADI method ⋮ Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations ⋮ Distributed solving linear algebraic equations with switched fractional order dynamics ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Residual-based iterations for the generalized Lyapunov equation ⋮ Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control ⋮ Near-optimal frequency-weighted interpolatory model reduction

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• Convergence of the iterative rational Krylov algorithm
• On the ADI method for Sylvester equations
• Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
• On \(H_2\) model reduction of bilinear systems
• On the decay rate of Hankel singular values and related issues
• Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
• On the ADI method for the Sylvester equation and the optimal-\({\mathcal H}_{2}\) points
• Algorithms for model reduction of large dynamical systems
• Efficient numerical solution of the LQR-problem for the heat equation
• A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations
• Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Approximate implicit subspace iteration with alternating directions for LTI system model reduction
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• Interpolation-Based ${\cal H}_2$-Model Reduction of Bilinear Control Systems
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Approximation of Large-Scale Dynamical Systems

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