Data-Driven Balancing of Linear Dynamical Systems
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Publication:5037546
DOI10.1137/21M1411081zbMath1492.37076arXiv2104.01006OpenAlexW3142899349MaRDI QIDQ5037546
Christopher A. Beattie, Ion Victor Gosea, Serkan Gugercin
Publication date: 1 March 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.01006
numerical quadraturetransfer functionsbalanced truncationimpulse responsesGramiansdata-driven modeling
Approximation by rational functions (41A20) Realizations from input-output data (93B15) Large-scale systems (93A15) Numerical integration (65D30) Approximation methods and numerical treatment of dynamical systems (37M99)
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- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Model order reduction for linear and nonlinear systems: a system-theoretic perspective
- Reduced-order models for control of fluids using the eigensystem realization algorithm
- Interpolatory weighted-\(\mathcal{H}_2\) model reduction
- Balancing for nonlinear systems
- Perturbation bounds for the Cholesky and QR factorizations
- Low-rank iterative methods for projected generalized Lyapunov equations
- A framework for the solution of the generalized realization problem
- Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals
- The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
- Numerical solution of generalized Lyapunov equations
- Data-driven structured realization
- A modified low-rank Smith method for large-scale Lyapunov equations
- A quadrature framework for solving Lyapunov and Sylvester equations
- \texttt{emgr} -- the empirical Gramian framework
- Self-generating and efficient shift parameters in ADI methods for large Lyapunov and Sylvester equations
- Balancing transformations for infinite-dimensional systems with nuclear Hankel operator
- Model Reduction of Bilinear Systems in the Loewner Framework
- Structure-Preserving Model Reduction for Integro-Differential Equations
- Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
- Data-Driven Parametrized Model Reduction in the Loewner Framework
- The Exponentially Convergent Trapezoidal Rule
- Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
- Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation
- Data‐driven model order reduction of quadratic‐bilinear systems
- Computational Methods for Linear Matrix Equations
- Parabolic and hyperbolic contours for computing the Bromwich integral
- Vector Fitting for Matrix-valued Rational Approximation
- A proper orthogonal decomposition approach to approximate balanced truncation of infinite dimensional linear systems
- Principal component analysis in linear systems: Controllability, observability, and model reduction
- Synthesis of minimum roundoff noise fixed point digital filters
- A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
- Model Reduction and Approximation
- Accuracy and Stability of Numerical Algorithms
- Low Rank Solution of Lyapunov Equations
- A Link Between Gramian-Based Model Order Reduction and Moment Matching
- Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms
- Quadrature-Based Vector Fitting for Discretized $\mathcal{H}_2$ Approximation
- MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION
- Model Order Reduction by Balanced Proper Orthogonal Decomposition and by Rational Interpolation
- Data-Driven Reduced Model Construction with Time-Domain Loewner Models
- Reduced Basis Methods for Partial Differential Equations
- Matrix Equation $XA + BX = C$
- Approximation of Large-Scale Dynamical Systems
- Balanced truncation for linear switched systems